The polynomial function P(x) of degree 5 has a leading coefficient of 1, Zeros of multiplicity 2 at x=3 and x=0, and a Zero of multiplicity 1 at x=-3

Question

The polynomial function P(x) of degree 5 has a leading coefficient of 1, Zeros of multiplicity 2 at x=3 and x=0, and a Zero of multiplicity 1 at x=-3

Find the polynomial function P(x). Leave your answer in factored form.

P(x)= _______________

Answer 1

Hello Chanel,

Since the polynomial has a zero of multiplicity 2 at x = 3, it means you'll have (x-3) (x-3) in your answer, which you can also write as (x-3)². Why x -3 and not x+3? Because each parenthesis is written as

(x - whatever_the_zero_is)

The polynomial also has a zero of multiplicity 2 at x = 0, so your polynomial will also have (x-0) (x-0), which is the same as x * x, which is the same as x².

The polynomial also has a zero of multiplicity 1 at x = -3, so only one (x - -3) which is (x + 3).

Finally, your polynomial has a leading coefficient of 1, so you can write P(x) as:

P(x) = 1 * x² * (x-3)² * (x+3) = x² • (x-3)² •(x+3)