Find the zeros of . What are their multiplicities?
Options
A
0 (multiplicity 2), 3
B
0 (multiplicity 4), 3 (multiplicity 2)
C
0 (multiplicity 3), 2, 1
D
0 (multiplicity 2), 1, 3
Answer & Analysis
Answer
D
Analysis
To find the zeros of the polynomial function and determine their multiplicities, we will go through the steps of factoring the polynomial and identifying the roots.
Step 1: Factor the polynomial
First, factor out the greatest common factor from the polynomial:
Next, we will factor the quadratic . We look for two numbers that multiply to ( 3 ) and add up to ( -4 ). The numbers ( -1 ) and ( -3 ) work:
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