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