Question

What are the zeros of this polynomial and state their multiplicity at each
y=(x-5)(x+2)^2

Answer 1

C.

Explanation:

The zeros of a polynomial are the x-intercepts of the function. To find them, we factor the polynomial and set each factor equal to 0.

This polynomial is already factored so set each to 0 and solve for x.

`x-5=0\\x=5\\(x+2)^(2)=0 \\(x+2)=0\\x=-2`

This means x=-2, 5. Each zero or root has a multiplicity - the number of times the factor occurs. This is also known as the exponent of the factor expression.

(x+5) occurs once since it has exponent 1.

`(x+2)^(2)` occurs twoce since it has exponent 2.

x=5 mult. 1, x=-2 mult. 2