consider the function (f(x)=(x - 3)^2(x + 2)^2(x - 1)). the zero has a multiplicity of 1. the zero -2 has a…

consider the function (f(x)=(x - 3)^2(x + 2)^2(x - 1)). the zero has a multiplicity of 1. the zero -2 has a multiplicity of

consider the function (f(x)=(x - 3)^2(x + 2)^2(x - 1)). the zero has a multiplicity of 1. the zero -2 has a multiplicity of

Answer

Explanation:

Step1: Recall zero - multiplicity concept

The multiplicity of a zero (a) of a polynomial (P(x)) is the exponent of the factor ((x - a)) in the factored form of (P(x)). Given (f(x)=(x - 3)^2(x + 2)^2(x - 1)).

Step2: Identify zero with multiplicity 1

For the factor ((x - 1)), when (x=1), (f(1) = 0) and the exponent of ((x - 1)) is 1. So the zero (1) has a multiplicity of 1.

Step3: Identify multiplicity of (x=-2)

For the factor ((x + 2)=(x-(-2))), the exponent of ((x + 2)) is 2. So the zero (-2) has a multiplicity of 2.

Answer:

The zero (1) has a multiplicity of 1. The zero (-2) has a multiplicity of 2.