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)#