Factor the polynomial
16x^2-48x+36

Question

Factor the polynomial
16x^2-48x+36

anonymous · Answer

oh wait...i did that wrong..

anonymous · Answer

This is  a perfect square trinomial.  To find the factors, first look at the first and last terms.  Notice that 16x^2 is (4x)^2 and 36 is 6^2.  The middle term is the result of taking twice the product of these two terms, resulting in a perfect square trinomial.  It factors as (4x+6)^2  Which can further be factored into (2(2x+3))^2 Finally, this simplifies to 4(2x+3)^2.

zehanz · Answer

If it was of the form a²-2ab+b², it could be written as (a-b)².

It certainly LOOKS like this!
After all, 16x² is the square of 4x,
36 is 6², so it could well be (4x-6)².

If we check the middle term (which should be -2ab) we have -2*4x*6 = -48x, so it is just right!

Now one extra number can be factored out: (4x-6)²=(2(2x-3))²=4(x-3)²

So my final answer would be: 

4(x-3)²

anonymous · Answer

Forgot the coefficient of x is 2, ZeHanz.

zehanz · Answer

Right you are, @calmat01 !

4(2x-3)²

anonymous · Answer

so it would be $$4(2x-3)^2$$

anonymous · Answer

yes.  That is correct!

anonymous · Answer

how would I show my work on this one?

anonymous · Answer

I got the answer, but it would be nice if I had some work shown to backer up haha!

anonymous · Answer

Never mind I got it! Thank you so much, this website has really been helping me out!