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

oliviayychengwh

oliviayychengwh

Answered question

2021-12-11

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

Answer & Explanation

Medicim6

Medicim6

Beginner2021-12-12Added 33 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)

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?