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

Coroware

Coroware

Answered question

2021-12-02

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)=x4+3x24

Answer & Explanation

huckelig75

huckelig75

Beginner2021-12-03Added 11 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)=x4+3x24
To find the real zeros of P(x):
P(1)=(1)4+3(1)24
=1+3-4=0
P(1)=0
P(1)=(1)4+3(1)24
=1+3-4=0
P(1)=0
Thus, x = -1 and x = 1 are the real zeros of P(x)=x4+3x24
Hence, P(x) can be factored as,
P(x)=(x1)(x+1)(x2+4)

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