Question

Factor the polynomial and use the factored form to find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)

P(x) = x^3 − x^2 − 20x
x =____.

Answer 1

To factor the given polynomial and find the zeros, we can set the polynomial equal to zero and solve for x. The factored form of the polynomial will be the product of the factors, and the zeros of the polynomial will be the values of x that make the polynomial equal to zero. In this case, the zeros are x = 0, x = 5, and x = -4.

Step-by-step explanation:

To factor the polynomial, we need to find the zeros of the polynomial first. The factored form of the polynomial will be the product of the factors (x - a)(x - b)(x - c), where a, b, and c are the zeros of the polynomial. To find the zeros, we need to set the polynomial equal to zero and solve for x.

Given polynomial: P(x) = x^3 - x^2 - 20x

Setting it to zero: x^3 - x^2 - 20x = 0

Factoring: x(x^2 - x - 20) = 0

We can further factor the quadratic factor to get:

x(x - 5)(x + 4) = 0

Thus, the zeros of the polynomial are x = 0, x = 5, and x = -4.