What is the completely factored form of x4 + 8x2 – 9?

ANSWER

EXPLANATION

The given function is

Split the middle term

Factor by grouping;

Factor further to get:

Apply difference of two squares to get:

Step-by-step explanation:

We would need to let u = x^2 and use middle term factorization first. let's do this:

if u = x^2, then x^4 + 8x^2 – 9 would be

u^2+8u-9

Middle term factorization of this is:

(u+9)(u-1)

now replacing back u = x^2:

(x^2+9)(x^2-1)

Using the formula a^2 - b^2 = (a+b)(a-b), we can write (x^2 - 1) as (x+1)(x-1).

So, the final factored form is:  (x^2+9)(x-1)(x+1)

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step-by-step explanation:

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