Question

Factor the polynomial expression x6 – x3 – 20

Answer 1

(x³ - 5)(x³ + 4)

Explanation:

Consider the factors of the constant term (- 20) which sum to give the coefficient of the x³ term (- 1)

The factors are - 5 and + 4, since

- 5 × 4 = - 20 and - 5 + 4 = - 1, hence

`x^(6)` - x³ - 20 = (x³ - 5)(x³ + 4)

Answer 2

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: