We want to find if x-1 is a factor of
[tex]f(x)=x^5+2x^2-1[/tex]In order to verify that, we must know the last number of the synthetic division of the polynomial divided by x - 1. If it is zero then it is a factor, and if it is not zero then it is not a factor
If we replace x = 1 in the equation we will find that number:
[tex]\begin{gathered} f(x)=x^5+2x^2-1 \\ f(1)=1^5+2\cdot1^2-1 \\ f(1)=1^{}+2^{}-1 \\ f(1)=2 \end{gathered}[/tex]Then the residual of the polynomial divided by x - 1 is 2, then x - 1 is NOT a factor.
