Question

What is the completely factored form of this polynomial x^4 + 12x^2 + 32

Answer 1

`(x^(2)+4)(x^(2)+8)`

Step-by-step explanation

We want to completely factor the given polynomial:

`x^4+12x^2+32`

To do this, we have to find two terms whose product is 32 and whose sum is 12.

The two terms are:

`x^4+8x^2+4x^2+32`

Now, factor completely:

`\begin{gathered} x^2(x^2+8)+4(x^2+8) \\ (x^2+4)(x^2+8) \end{gathered}`

That is the answer.