Question

1. what is the multiplicity of the zero at x = 1 in the polynomial r(x) = (x - 1)³(x + 2)?

a. 2
b. 1
c. 4
d. 3

Explanation:

Step1: Recall the definition of multiplicity

The multiplicity of a zero \( x = a \) in a polynomial is the exponent of the factor \( (x - a) \) in the factored form of the polynomial.

Step2: Identify the factor for \( x = 1 \)

In the polynomial \( R(x)=(x - 1)^{3}(x + 2) \), the factor corresponding to the zero \( x = 1 \) is \( (x - 1) \).

Step3: Determine the multiplicity

The exponent of \( (x - 1) \) is 3. So, the multiplicity of the zero at \( x = 1 \) is 3.

Answer:

d. 3