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Chapter 2: Problem 2

Find the zeros of the polynomial function and state the multiplicity of each zero. $$P(x)=(x+4)^{3}(x-1)^{2}$$

Short Answer

Expert verified
The zeros of the function are -4 (with multiplicity 3) and 1 (with multiplicity 2)

Step by step solution

01

Identify the zeros

The zeros of the polynomial function are the values of \(x\) for which the function equals zero. For the function \(P(x)=(x+4)^{3}(x-1)^{2}\), the zeros are -4 and 1. That's because, for these values, \(P(x)\) is equal to zero.
02

Identify the multiplicity

The multiplicity of a zero of a polynomial function is the number of times that zero occurs as a root. In other words, it's the exponent of the factor that represents that zero. In \(P(x)=(x+4)^{3}(x-1)^{2}\), the zero -4 has a multiplicity of 3 because it is represented by the factor \((x+4)^{3}\), while the zero 1 has multiplicity of 2 because it is represented by the factor \((x-1)^{2}\)

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