Objective - To factor trinomials in the form . x2 + bx + c

Factoring when c is positive.x2 + bx + cMultiply.(x + 3)(x + 2) = x2 + 5x + 6

sum product

Last Terms

Sum ofLast

Terms

Productof Last Terms

Factor.x2 + 7x +10 = ( )( )x x+ + 1•10

2 •52 5(x + 2)(x + 5)

Factor.

1)

2)

x2 + 9x + 20

y2 − 8y+12

= ( )( )x x+ +1•202 •104 54 •5

= ( )( )y y 1•122 •62 62)

3)

y − 8y+12

m2 − 7m +12

= ( )( )y y 2 •62 63• 4

− −

= ( )( )m m 1•122 •63 43• 4

− −

( )( )

( )( )=

Factor. Show factor pairs of the constant term.

1)

2)

3)

x2 +13x + 42

m2 −10m+ 21

y2 15y + 36

x x+ +1• 422 •216 7 3•146 • 7

= ( )( )m m 1•213 7 3• 7− −

y y1• 36

3 122 •183•12= ( )( )

= ( )( )x x

3)

4)

5)

y −15y + 36

k2 +12k + 24

x2 −11x + 24

y y3 12− − 3•124 •96 •6

= ( )( )k k1•242 •123•84 •6Not Factorable

3 8− −1•242 •123•84 •6

+ +

Factoring when c is negative.x2 + bx + c

Multiply.(x + 5)(x − 2) = x2 + 3x − 10

Last Terms

Differenceof Last T

Productof Last T

difference product

Terms TermsFactor.

x2 + 4x −12 = ( )( )x x+ 1•122 •66 2

(x + 6)(x − 2)−

3• 4

Factor.

1)

2)

x2 + x−12

y2 − 3y − 40

= ( )( )x x+1•122 •64 33• 4

= ( )( )y y1• 402 •205 8

−

+2)

3)

y − 3y − 40

t 2 − 7t −18

= ( )( )y y5 8 4 •10−

= ( )( )t t 1•182 •92 93•6

−

+5 •8

+

Factor. Show factor pairs of the constant term.

1)

2)

3)

m2 + 3m− 28

x2 − x − 30

k2 2k 24

= ( )( )m m+1•282 •147 4 4 • 7

= ( )( )x x1• 30

5 6 2 •15−

( )( )k k1•24

4 6 2 •12

−

+ 3•105 •6

+

= ( )( )p2 p2

3)

4)

5)

k − 2k − 24

t 2 + 5t −18

p4 − 2p2 − 35

= ( )( )k k4 6− 3•84 •6

= ( )( )t t 1•182 •93•6

Not Factorable

5 7− 1• 355 • 7

+

+

−

+

Lesson 8-3

Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Factor.1)

2)

5)

6)

x2 + 8x + 7

x2 −14x + 24

2t 6t 5+ +

x2 − 4x − 451 7

2 12

1 5

5 9

(x )(x )+ + 1 7•

(x )(x )− −1 24•2 12•3 8•4 6

(t )(t )+ + 1 5•

(x )(x )+ − 1 45•3 15•5 9•

3)

4)

7)

8)

y2 − 5y−14

x2 + 3x−10

2 2a 10ab 24b− −

x2 −13xy +12y22 7

5 2

2b 12b

1y 12y

4 6•

(y )(y )+ − 1 14•2 7•

(x )(x )+ − 1 10•2 5•

5 9•

(a )(a )+ −1 24•2 12•3 8•4 6•

(x )(x )− − 1 12•2 6•3 4•

Factoring Polynomials

2) Trinomial Factoring : 2x bx c+ +

Five Types of Factoring

1) Greatest Monomial Factor (Group) 1) Greatest Monomial Factor (Group)

2) Trinomial Factoring : 2x bx c+ +

3) Trinomial Factoring : 2ax bx c+ +

4) Perfect Square Trinomial

5) Difference of Squares

Factor completely.1) 3x2 + 21x + 36

3(x2 + 7x +12) Greatest Monomial FactorFactoring3(x + )(x + )

1•122 •63• 443 x2 + bx + c

2) 4 22x 18x 36− +

Factoring2 22(x )(x )− − 1 18•2 9•63 x2 + bx + c

42(x 9x 18)− + Greatest Monomial Factor

3 6•

Factor completely.3) y3 − 5ay2 + 6a2y

y(y2 − 5ay + 6a2) Greatest Monomial FactorFactoringy(y − 2a)(y − 3a) 1•6

2 • 3 x2 + bx + c

4) 6 4 22a 24a 70a− +

Factoring2 2 22a (a )(a )− − 1 35•5 7•75 x2 + bx + c

2 4 22a (a 12a 35)− + Greatest Monomial Factor

Lesson 8-3 (cont.)

Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010