The polynomial y=x^{5}+x^{3}-x^{2}-1 factors into (x^{2}+1)(x^{3}-1). What is the multiplicity

Talamancoeb

Talamancoeb

Answered question

2021-12-06

The polynomial y=x5+x3x21 factors into (x2+1)(x31). What is the multiplicity of the root (x31)?
a. 3
b. 2
c. 1
d. 5

Answer & Explanation

Becky Harrison

Becky Harrison

Beginner2021-12-07Added 40 answers

Step 1 
Polynomial y=x5+x3x21 
Factored form: (x2+1)(x31) 
Equate (x31)=0 
+1 +1 
x3=1 
Taking cuberoot on both the sides, 
x=1 (Zero) 
According to the algebraic fundamental theorem, the multiplicity of a root is the number of times it appears in the polynomial's complete factorization.

As the power of (x31) is 1. Therefore, its multiplicity is 1. 
Step 2 
Ans: 
Multiplicity of the root (x31) is 1. 
So, the correct option is (c).

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?