Let P(x)=x^{3}-3x^{2}+x-3 Find all the zeros of P. Find the complete factorization of P.

Emeli Hagan

Emeli Hagan

Answered question

2021-05-28

Let P(x)=x33x2+x3
Find all the zeros of P.
Find the complete factorization of P.

Answer & Explanation

dieseisB

dieseisB

Skilled2021-05-29Added 85 answers

Step 1
Given, P(x)=x33x2+x3
For zeroes substituting,P(x)=0
x33x2+x3=0
On simplifying further we get:
x33x2+x3=0
x2(x3)+(x3)=0
(x3)(x2+1)=0
(x3)=0,or,(x2+1)=0
x=3, or, x=±1
x=3, or, x=±i (using, 1=i)
Hence, zeroes are:x=(3,±i)
Step 2
Required factorizes form is:
P(x)=x33x2+x3=(x2+1)(x3)

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