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) = x3 − 2x2 − 15x
x =

Answer 1

-3, 0, 5

Explanation:

You want the zeros of P(x) = x³ − 2x² − 15x using the factored form.

Factored form

We notice right away that x is a factor of every term. Factoring that out gives us a quadratic to factor:

P(x) = x(x² -2x -15)

To factor this, we need two factors of -15 that have a sum of -2. The factors -5 and +3 have those properties. That means our factored form is ...

P(x) = x(x +3)(x -5) . . . . factored form

Zeros

This product will be zero when any of its factors is zero. Considering them one at a time, we find the zeros of P(x) to be ...

x = 0

x +3 = 0 ⇒ x = -3

x -5 = 0 ⇒ x = 5

The zeros of P(x) are -3, 0, 5.