How do you write x³+8x²+16x in factored form?

1 Answer
Mar 2, 2018

Answer:

#x(x+4)(x+4)#

Explanation:

Note that all terms include an instance of #x.# Thus, we can factor out #x:#

#x^3+8x^2+16x=x(x^2+8x+16)#

We now have a single term and a quadratic equation. Let's factor the quadratic #x^2+8x+16#.

We must find two numbers, #a# and #b#, which multiply together to give #16# and add together to give #8# to factor our quadratic into the form #(x+a)(x+b)# . Note that #a# and #b# can be the same number.

That would be #4, 4#, as #4*4=16,4+4=8#

So, the factored form of our quadratic is #x^2+8x+16=(x+4)(x+4)#

#x(x^2+8x+16)=x(x+4)(x+4)#