Question

Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

f(x) = 2(x + 7)(x + 5)(x – 2)

f(x) = 2(x – 7)(x – 5)(x + 2)

f(x) = (x + 7)(x + 5)(x + 5)(x – 2)

f(x) = (x – 7)(x – 5)(x – 5)(x + 2)

Answer 1

f(x) = (x -7)(x - 5) {(x - 5)}(x + 2) the answer is D

Explanation:

Answer 2

`f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)`

EXPLANATION

If the polynomial has a root -2, with multiplicity 1, then (x+2) is a factor.

If the polynomial has root, 7 with multiplicity 1, then (x-7) is a factor.

If the polynomial has root 5, with multiplicity 2, then (x-5)² is a factor of the polynomial.

The fully factored form of the polynomial is

`f(x) =a (x + 2)(x - 7) {(x - 5)}^(2)`

It was given that the polynomial has a leading coefficient of 1.

Hence a=1.

This implies that,

`f(x) =(x + 2)(x - 7) {(x - 5)}^(2)`

Or

`f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)`