Question

solve:
x^4-13x^2+36=0

Answer 1

A trinomial with varying degrees in equal increments may be factored out just as y=ax^2+bx+c can be, except the degrees are multiplied by the increment it is increased.
Let's make it easy on ourselves first. Let's knock it down to x^2-13x+36. Do you know how to solve such an equation?

Answer 2

yah, it would be (x-9)(x-4) ?

Answer 3

Correct. Now this little trick can only be done with trinomials that follow a degree-increment decrease. Since your equation is double what is normally used (y=ax^2+bx+c), then the powers of only the x values double, so you will end up with (x^2-9)(x^2-4).

Had this been something like x^6-13x^3+36, then it would be (x^3-9)(x^3-4)
Or: x^8-13x^4+36, then it would be (x^4-9)(x^4-4).

Do you understand this shortcut?

Answer 4

yah, thank you that makes it way easier:)