What is the completely factored form of x^4+8x^2-9

Remark

You'll see it a whole lot easier if you make a substitution so that it looks like something you have already seen

Solution

let y = x^2

x^4 = x^2 * x^2

x^4 = y * y

x^4 = y^2

Now the expression becomes

y^2 + 8 y - 9 = z

(y + 9) (y - 1) = z

Now put the x^2 back in.

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

x^2 - 1 becomes x + 1 and x - 1. At this level x^2 + 9 can't be factored.

Answer

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

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