Question

Factor x2 – 8x + 15. Which pair of numbers has a product of ac and a sum of b?

Answer 1

AC = (-5)(-3)
sum = -8

x^2 - 5x - 3x + 15
x(x-5)-3(x-5)
(x-3) (x-5)

x=3 x=5

Answer 2

Answer:

Pair of numbers: -3 and -5

Factors : (x-5)(x-3)

Step-by-step explanation:

Given: $x^2-8x+15$

We need to factor it using AC method.

For equation: $ax^2+bx+c$

For factor this ac and sum b

For our equation: a=1, b=-8 and c=15

Therefore,

Product = ac = (1)(15) = 15

We need to choose two number whose product is 15 and sum -8

First we find all the factor of 15: 1x15    3x5    

If we take 3x5

Product:  (-3)(-5) = 15

Sum:          -3-5  = -8

Pair of numbers: (-3,-5)

Now we will factor it.

$\Rightarrow x^2-8x+15$

$\Rightarrow x^2-5x-3x+15$

$\Rightarrow (x^2-5x)+(-3x+15)$

$\Rightarrow x(x-5)-3(x-5)$

$\Rightarrow (x-5)(x-3)$

The factors are (x-5) and (x-3)