Factoring into Binomials
X2 + 10x + 16
Our goal is to get this into two different
binomials (x+a)(x+b) = x2 + 10x + 16.
(x+a)(x+b) = x2+(a+b)x+ab = x2+10x+16
so (a+b) = 10
ab = 16
X2 + 10x + 16
(x+a)(x+b) = x2+(a+b)x+ab = x2+10x+16
so (a+b) = 10
ab = 16
What are the factors of 16 that add to 10?
16: 1,2,4,8,16
10 = 2 + 8
Answer: (x+2)(x+8)
x2+3x-10
What are the factors of -10 that add to 3?
-10: -1,1,-2,2,-5,5,-10,10
3= -2 + 5
Answer: (x-2)(x+5)
x2-10x-24
What are the factors of -24 that add to -10?
3x2+7x+4
First, set up the binomials so that the coefficient from the
“x2” term is in both of the terms…
(3x+a)(3x+b)
Second, multiply the coefficient from the “x2” term (3)
with the constant term (4).
3 X 4 = 12
Then ask, what factors of 12 add to 7?
12: 1, 2, 3, 4, 6, 12
7= 3+4
Third, put in your solutions and take out and remove any
common factors:
(3x+3)(3x+4) = (x+1)(3x+4)
Feb. 11 Practice
Factor:
1) 2x2+7x+3
2) 3x2-4x+4
Feb. 11 Practice
3) 2x2+9x+7
4) 5x2+2x-3
Feb. 11 Practice
5) 4x2-5x-6
6) 6x2+29x+9
Feb. 11 Practice
7) 2x2-9x+9
8) 2x2+11x+12
Feb. 11 Practice
9) 3x2+7x+2
10) 8x2+31x-4