Question

5. Is X-1 a factor of x^5+2x^2-1?No, because f(1) = 2.Yes, because f(1) = 3.No, because f(1) = 0.Yes, because f(1) = 0.

Answer 1

Finding a factor of a polynomial

We want to find if x-1 is a factor of

`f(x)=x^5+2x^2-1`

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:

`\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}`

Then the residual of the polynomial divided by x - 1 is 2, then x - 1 is NOT a factor.

Answer: A No, because f(1) = 2.