Question

How do you factor `x^4 - 20x^2 + 64`?

Answer 1

Factor of the bi-quadratic function: f(x) = x^4 - 20x^2 + 64.

Ans: f(x) = (x - 2)(x + 2)(x - 4)(x + 4)

Explanation:

Call x^2 = X --> f(X) = X^2 - 20X + 64.= (X + p)X + q).
p and q havs same sign. Factor pairs of (64) --> (2, 32)(4, 16). This sum is 20 = -b. The opposite sum gives: p = -4 and q = -16.
Factored form `f(x) = (X - 4)(X - 16) = (x^2 - 4)(x^2 - 16) =`
`= (x - 2)(x + 2)(x - 4)(x + 4).`