Question

Factor the polynomials to find if x - 5 is a root of the polynomial x^3 - 2x^2 - 13x - 10. (Use synthetic division or long division). Picture attached and answer options below.

Answer 1

Option (3)

Explanation:

Given polynomial is (x³ - 2x² - 13x - 10).

If (x - 5) is a factor of the given polynomial, other factors can be found by the synthetic division.

5) 1 -2 -13 -10

- 5 15 10

1 3 2 0

Therefore, other factor of the given polynomial will be (x² + 3x + 2)

And the factored form of the polynomial will be,

(x - 5)(x² + 3x + 2)

Option (3) will be the answer.