objectives: students will be able to… write a polynomial in factored form apply special...
TRANSCRIPT
Objectives:Students will be able to… Write a
polynomial in factored form
Apply special factoring patterns
5.2: PART 1- FACTORING
1. What 2 numbers multiply together to get 24 and have a sum of 10?
2. What is the definition of a factor of a number?
WARM UP:
The process of breaking down a product into the quantities that multiply together to get the product
In essence, you are reversing the multiplication process
When factoring polynomials, you are breaking it up into simpler terms; breaking it into the terms that multiply together to get the polynomial
FACTORING
The largest factor that divides evenly into a quantity In a polynomial, the GCF must be common to ALL
terms. Divide out the GCF (do not drop it!!!!!!!!!!!!!!)
EXAMPLES: Factor
GREATEST COMMON FACTOR (GCF)
245
2
23
3
2
.5
22.4
24126.3
105.2
128.1
xxx
t
mmm
dd
xx
x2 + bx + cWhen a = 1, EASY!!!!Look for factor pairs of c that add up to bBe aware of signs
FACTORING TRINOMIALS
EXAMPLES: FACTOR
22
2
2
2
2411.7
208.5
1811.3
107.1
yxyx
mm
xx
gg
22
2
2
2
6017.8
56.6
3615.4
3013.2
nmnm
yy
aa
ax2 + bx +c , where a ≠ 1
1. 2y2 + 5y +2 2. 6n2 -23n +7
FACTORING TRINOMIALS
3. 5d2 -14d -3 4. 20p2 -31p -9
5. 3d2-17d+20
EXAMPLES, CONT.
Always look for GCF fi rst. If it has one, factor it out and try to factor what remains in parenthesis. DO NOT DROP GCF!!!!!!!
EXAMPLES: Factor
FACTORING COMPLETELY
kkk
yy
vv
61218.3
6144.2
10122.1
23
2
2
Diff erence between 2 perfect squares: a2 – b2 = (a + b) (a – b)
For example: x2 – 9 = (x + 3)(x – 3)
4x2 – 25 = (2x + 5)(2x -5)
SPECIAL FACTORING CASES
Perfect Square Trinomials:
a2 + 2ab + b2 = (a +b)(a +b) = (a+ b)2
a2 – 2ab + b2 = (a –b) (a- b) = (a –b)2
For example:
x2 + 8x + 16 = (x + 4)(x +4) = (x + 4)2
x2 - 8x + 16 = (x - 4)(x -4) = (x - 4)2
SPECIAL FACTORING PATTERNS, CONT.
Hint…How to recognize pattern:
1. The first & last terms are perfect squares
2. The middle term is twice the product of one factor from first term & one factor from last term.
1. n2 + 16n +64
2. 9q2 – 12q + 4
3. 4t2 + 36t +81
4. p2 – 49
5. 16x2 – 25
6. 81- x2
EXAMPLES: FACTOR
1. 5x2 -20
2. 6k2 + 12k +6
3. 48y3 – 24y2 + 3y
4. x2 + 5x +16
5. -4x2 – 4x + 24
6. 3r3 – 48rs2
7. - x2 + 11x +42
FACTOR COMPLETELY, IF POSSIBLE