How do you factor 4x^2-32x+60?

2 Answers
Mar 3, 2018

factor out 4

4(x^2-8x+15)

what numbers add up to -8 and multiply to 15?
-3 and -5

4(x-3)(x-5)

Mar 3, 2018

4x^2-32x +60 = (2x-6)(2x-10)

Explanation:

We can write that trinomial as

4x^2 - 32x + 60 = 4x^2 - 32x + 64 - 4

Now,
4x^2 - 32x + 64 = (color(red)(2x))^2 - 2*color(red)(2x)*color(red)8 + color(red)8^2

Knowing that
(a-b)^2 = a^2-2ab+b^2

We can deduce 4x^2 - 32x + 64 to be a perfect square, precisely color(red)((2x-8)^2).

Substitute it into the original expression :

4x^2 - 32x + 64 - 4 = (2x-8)^2 - 2^2

That is a difference of squares, so we can factor it out as:

(2x-8color(red)+ 2)(2x-8color(red)-2) = color(blue)((2x-6)(2x-10)