Show all work to factor x4 – 10x^2 + 9 completely.

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

Step-by-step explanation:

it is a fourth degree trinomial

1) find two number whose sum is -10 and whose product is 9

the two numbers are -1 and -9

2) write the trinomial as a multiplication in this way

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

3) the two factors are both a difference of tho squares.

so we can rewrite it as

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