How do you determine whether x-1 is a factor of the polynomial 4x^4-2x^3+3x^2-2x+14x42x3+3x22x+1?

1 Answer

See explanation.

Explanation:

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

So to check if (x-1)(x1) is a factor of P(x)=4x^4-2x^3+3x^2-2x+1P(x)=4x42x3+3x22x+1 you have to check if P(1)=0P(1)=0

P(1)=4*1^4-2*1^3+3*1^2-2*1+1=4-2+3-2+1P(1)=414213+31221+1=42+32+1

P(1)=4P(1)=4

P(1)P(1) is not zero, so (x-1)(x1) is not the factor of P(x)P(x)

In fact P(1)=4P(1)=4 means that the remainder when 4x^4-2x^3+3x^2-2x+14x42x3+3x22x+1 is divided by x-1x1 is 44