Write a polynomial f(x) that meets the given conditions. Polynomial of

Monique Slaughter 2021-12-13 Answered
Write a polynomial f(x) that meets the given conditions.
Polynomial of lowest degree with zeros of -1 (multiplicity 2) and -4 (multiplicity 2) and with f(0)=32
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Expert Answer

Robert Pina
Answered 2021-12-14 Author has 42 answers
Step 1
x=-1 is a zero so (x+1) is a factor. It has multiplicity = 2 , so (x+1)2 is a factor of the polynomial f(x).
x=-4 is a zero so (x+4) is a factor. It has multiplicity = 2 , so (x+4)2 is a factor of the polynomial f(x).
Step 2
Let f(x)=k(x+1)2(x+4)2
Given f(0)=32. Using this we find k.
f(x)=k(x+1)2(x+4)2
f(0)=k(0+1)2(0+4)2
32=k(1)2(4)2
32=16k
k=3216
k=2
f(x)=2(x+1)2(x+4)2
Answer: f(x)=2(x+1)2(x+4)2.
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