Complete Factorization. A polynomial function P is given. Find all

grislingatb

grislingatb

Answered question

2021-12-05

Complete Factorization. A polynomial function P is given. Find all the real zeros of P, and factor P completely into linear and irreducible quadratic factors with real coefficients
P(x)=x32x4

Answer & Explanation

Befoodly

Befoodly

Beginner2021-12-06Added 17 answers

Step 1
To find all the real zeros of P, and to factor P completely into linear and irreducible quadratic factors with real coefficients.
Step 2
Given:
P(x)=x32x4
To find the real zeros of P(x):
P(2)=232(2)4
=8-4-4=0
P(2)=0
Thus, x = 2 is the zero of P(x)=x32x4.
Hence P(x) can be factored as,
P(x)=(x2)(x2+2x+2)

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