How do you determine whether x-1 is a factor of the polynomial #4x^4-2x^3+3x^2-2x+1#?

1 Answer
Daniel L. · Shwetank Mauria
Feb 17, 2017

See explanation.

Explanation:

According to The Remainder Theorem #(x-a)# is a factor of a polynomial #P(x)# if and only if #P(a)=0#.

So to check if #(x-1)# is a factor of #P(x)=4x^4-2x^3+3x^2-2x+1# you have to check if #P(1)=0#

#P(1)=4*1^4-2*1^3+3*1^2-2*1+1=4-2+3-2+1#

#P(1)=4#

#P(1)# is not zero, so #(x-1)# is not the factor of #P(x)#

In fact #P(1)=4# means that the remainder when #4x^4-2x^3+3x^2-2x+1# is divided by #x-1# is #4#

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