Which of the following is a factor of the polynomial 2x² - 3x - 5? (x + 1) or (x + 2).

Solution:

We will use the concept of the factor theorem in order to find the factor of the polynomial.

The factor theorem states that if (x - a) is the factor of the polynomial ax² + bx + c, then on substituting x = a in the polynomial if the result is 0 then (x - a) is the factor of the polynomial ax² + bx + c.

Now for the polynomial p(x) = 2x² - 3x - 5 when we substitute x = -1 in the polynomial then p(-1) = 0.

Hence, (x + 1) is the factor of the polynomial p(x).

If we substitute x = - 2 in the polynomial then p(-2) = -3.

Hence, (x + 2) is not the factor of the polynomial p(x).

Therefore, (x + 1) is the factor of the polynomial 2x² - 3x - 5.

Which of the following is a factor of the polynomial 2x² - 3x - 5? (x + 1) or (x + 2).

Summary:

(x + 1) is the factor of the polynomial 2x² - 3x - 5