Question

Let P be a polynomial function, and P(x)=x4-4x3+8x2-14x+16. Is (x-2) a factor of the polynomial, how can you tell?

Answer 1

`x - 2` is not a factor of the polynomial.

Explanation:

If
`x - 2` is a factor of the polynomial
`P(x) = x^(4)-4\cdot x^(3)+8\cdot x^(2)-14\cdot x +16`, then
`P(2) = 0`.

Now we evaluate the function:

`x = 2`

`P(2) = 2^(4)-4\cdot (2)^(3)+8\cdot (2)^(2)-14\cdot (2)-16`

`P(2) = -28`

Therefore,
`x - 2` is not a factor of the polynomial.