Question

Factor the polynomial expression x6 − x3 − 20.

Answer 1

Ask: Which two numbers add up to -1 and multiply to -20?

-5 and 4

Rewrite the expression using the given information above.

(x^3 - 5)(x^3 + 4)

Answer 2

Answer: x6 − x3 − 20 = (x3)2 − x3 − 20 = (x3 + 4)(x3 − 5)

Explanation: In this trinomial, the exponent of the first term, 6, is double the exponent in the second term, 3. And, the third term contains no variables. So, we can factor the expression as we would a quadratic, but treating x3 as if it were x: