Factor the polynomial completely, and find all its zeros. State

Wanda Kane

Wanda Kane

Answered question

2021-12-10

Factor the polynomial completely, and find all its zeros. State the multiplicity of each zero.
P(x)=x3+x2+9x+9

Answer & Explanation

Pansdorfp6

Pansdorfp6

Beginner2021-12-11Added 27 answers

Step 1
The Given Polynomial P(x)=x3+x2+9x+9
P(x)=x3+x2+9x+9
P(x)=x(x2+9)+1(x2+1)
P(x)=(x2+9)(x+1)
find the zeros of P by setting each factor equal to 0
P(x)=(x2+9)(x+1)
let,
x+1=0
x=-1
Step 2
so,
(x2+9)(x+1)=0
(x2+9)(1+1)=0
x2+9=0
x=±3i
therefore, the zero of P are (1,±3i)
by factorization theorem:
p(x)=(x+1)(x-3i)(x+3i)
thus polynomial P(x) has the following zeros
-1 (multiplicity of 1)
3i (multiplicity of 1)
-3i (multiplicity of 1)

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