Question

Show all work to factor x4 − 10x2 + 9 completely.

Answer 1

Explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a² - b² =(a+b)(a−b) where a=x and b=3.

(x+3)(x-3)(x+1)(x-1)

Answer 2

(x+1)(x-1)(x+3)(x-3)

Explanation:

x4-10x^2+9

Group expression so that the coefficients of the x^2 terms add up to +9.

= x^4 -9x^2 - x^2+9

match coefficients in both groups

= x^4 -9x^2 - (x^2-9)

factor each group

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

now factor out the common factor (x^2-9)

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

Finally, factor each quadratic factor

= (x+1)(x-1)(x+3)(x-3)