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4.1.4 - Factorisation II - Quadratics
4.1 - Algebra - Expressions
Leaving Certificate Mathematics
Higher Level & Ordinary Level
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 1 / 5
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A Quadratic Expression is one of the form ax2 + bx + c ,
where a, b, care numbers, a 6= 0
e.g. 4x2 + 8x + 3
Here,
a = 4
b = 8
c = 3
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 2 / 5
![Page 3: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/3.jpg)
A Quadratic Expression is one of the form ax2 + bx + c , where a, b, care numbers,
a 6= 0
e.g. 4x2 + 8x + 3
Here,
a = 4
b = 8
c = 3
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 2 / 5
![Page 4: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/4.jpg)
A Quadratic Expression is one of the form ax2 + bx + c , where a, b, care numbers, a 6= 0
e.g. 4x2 + 8x + 3
Here,
a = 4
b = 8
c = 3
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 2 / 5
![Page 5: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/5.jpg)
A Quadratic Expression is one of the form ax2 + bx + c , where a, b, care numbers, a 6= 0
e.g. 4x2 + 8x + 3
Here,
a = 4
b = 8
c = 3
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 2 / 5
![Page 6: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/6.jpg)
A Quadratic Expression is one of the form ax2 + bx + c , where a, b, care numbers, a 6= 0
e.g. 4x2 + 8x + 3
Here,
a = 4
b = 8
c = 3
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 2 / 5
![Page 7: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/7.jpg)
A Quadratic Expression is one of the form ax2 + bx + c , where a, b, care numbers, a 6= 0
e.g. 4x2 + 8x + 3
Here,
a = 4
b = 8
c = 3
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 2 / 5
![Page 8: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/8.jpg)
A Quadratic Expression is one of the form ax2 + bx + c , where a, b, care numbers, a 6= 0
e.g. 4x2 + 8x + 3
Here,
a = 4
b = 8
c = 3
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 2 / 5
![Page 9: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/9.jpg)
General method to factorise ax2 + bx + c :
1 Write out all factors of a× c .2 Choose a pair that will sum to give you b.
If c > 0, same sign (both + or both −)If c < 0, different signs (one +, one −)
3 Rewrite original expression.
4 Factorise!
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5
![Page 10: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/10.jpg)
General method to factorise ax2 + bx + c :
1 Write out all factors of a× c .
2 Choose a pair that will sum to give you b.
If c > 0, same sign (both + or both −)If c < 0, different signs (one +, one −)
3 Rewrite original expression.
4 Factorise!
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5
![Page 11: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/11.jpg)
General method to factorise ax2 + bx + c :
1 Write out all factors of a× c .2 Choose a pair that will sum to give you b.
If c > 0, same sign (both + or both −)If c < 0, different signs (one +, one −)
3 Rewrite original expression.
4 Factorise!
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5
![Page 12: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/12.jpg)
General method to factorise ax2 + bx + c :
1 Write out all factors of a× c .2 Choose a pair that will sum to give you b.
If c > 0, same sign (both + or both −)
If c < 0, different signs (one +, one −)
3 Rewrite original expression.
4 Factorise!
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5
![Page 13: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/13.jpg)
General method to factorise ax2 + bx + c :
1 Write out all factors of a× c .2 Choose a pair that will sum to give you b.
If c > 0, same sign (both + or both −)If c < 0, different signs (one +, one −)
3 Rewrite original expression.
4 Factorise!
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5
![Page 14: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/14.jpg)
General method to factorise ax2 + bx + c :
1 Write out all factors of a× c .2 Choose a pair that will sum to give you b.
If c > 0, same sign (both + or both −)If c < 0, different signs (one +, one −)
3 Rewrite original expression.
4 Factorise!
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5
![Page 15: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/15.jpg)
General method to factorise ax2 + bx + c :
1 Write out all factors of a× c .2 Choose a pair that will sum to give you b.
If c > 0, same sign (both + or both −)If c < 0, different signs (one +, one −)
3 Rewrite original expression.
4 Factorise!
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5
![Page 16: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/16.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
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Example 1
Q. Factorise 6x2 + 11x − 10
Answer:
a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 18: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/18.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6,
b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 19: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/19.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11,
c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 20: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/20.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 21: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/21.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c
= 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 22: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/22.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 23: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/23.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 24: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/24.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 25: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/25.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 26: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/26.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 27: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/27.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 28: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/28.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 29: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/29.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 30: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/30.jpg)
Example 1
Q. Factorise 6x2 + 11x − 10
Answer:a = 6, b = 11, c = −10
a× c = 6(−10)
= −60
Factors of 60:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 4 / 5
![Page 31: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/31.jpg)
6x2 + 11x − 10 =
6x2 + 15x − 4x − 10
= 3x(2x + 5) (2x + 5)
= (2x + 5)(3x − 2)
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 5 / 5
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6x2 + 11x − 10 = 6x2 + 15x − 4x − 10
= 3x(2x + 5) (2x + 5)
= (2x + 5)(3x − 2)
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 5 / 5
![Page 33: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/33.jpg)
6x2 + 11x − 10 = 6x2 + 15x − 4x − 10
= 3x(2x + 5)
(2x + 5)
= (2x + 5)(3x − 2)
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 5 / 5
![Page 34: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/34.jpg)
6x2 + 11x − 10 = 6x2 + 15x − 4x − 10
= 3x(2x + 5) (2x + 5)
= (2x + 5)(3x − 2)
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 5 / 5
![Page 35: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/35.jpg)
6x2 + 11x − 10 = 6x2 + 15x − 4x − 10
= 3x(2x + 5) (2x + 5)
= (2x + 5)
(3x − 2)
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 5 / 5
![Page 36: 4.1.4 - Factorisation II - Quadratics · 4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 3 / 5. General method to factorise ax2 + bx](https://reader035.vdocuments.site/reader035/viewer/2022062415/5fe2575780d9e32a45087df9/html5/thumbnails/36.jpg)
6x2 + 11x − 10 = 6x2 + 15x − 4x − 10
= 3x(2x + 5) (2x + 5)
= (2x + 5)(3x − 2)
4.1 - Algebra - Expressions 4.1.4 - Factorisation II - Quadratics Higher Level & Ordinary Level 5 / 5