Question

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

Answer 1

`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)`