Find the complete factorization of P(x)= x^{4} - 2x^{3} + 5x^{2} - 8x + 4.

glasskerfu

glasskerfu

Answered question

2021-06-03

Find the complete factorization of P(x)=x42x3+5x28x+4.

Answer & Explanation

firmablogF

firmablogF

Skilled2021-06-04Added 92 answers

Step 1
Given:
x42x3+5x28x+4
Step 2
x42x3+5x28x+4
Let p(x)=x42x3+5x28x+4
let x=1x1=0
p(1)=(1)42(1)3+5(1)28(1)+4
p(1)=12+58+4
p(1)=0
x1 is the factor of p(x)
x42x3+5x28x+4=(x1)(x3x2+4x4)
x42x3+5x28x+4=(x1)(x2(x1)+4(x1))
x42x3+5x28x+4=(x1)(x2+4)(x1)
x42x3+5x28x+4=(x1)2(x2+4)

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