Question

Use the Rational Root theorem to determine the factors of x^3 - 2x^2 - 13x - 10 given that one factor is (x + 1)

Answer 1

The correct option is;

D. (x - 5)·(x + 2)·(x + 1)

Explanation:

The Rational Root theorem is expressed mathematically as follows;

`Possible \ rational \ roots = (Factors \ of \ the \ constant \ term)/(Factors \ of \ the \ leading \ coefficient)`

The given polynomial is presented as follows;

x³ - 2·x² - 13·x - 10

A factor of the polynomial = (x + 1)

The factors of the constant term, -10 = -10, -5, -2, -1, 10, 5, 2, and 1

The factors of the leading coefficient, (the coefficient of the variable having the highest degree or power, x³) = 1

Given that (x + 1) is a known factor, the other two factors are either (x + 5) and (x - 2) or (x - 5) and (x + 2)

The option, that combines (x + 1) and the other two factor combination is (x - 5)·(x + 2)·(x + 1)

∴ The solution which meets the condition is (x - 5)·(x + 2)·(x + 1)

We check;

(x - 5)·(x + 2)·(x + 1) = x³ - 2·x² - 13·x - 10