Question

Determine the following polynomial has (x + 1) a factor:

`x^3-x^2-(2+sqrt2)x+sqrt2`

Answer 1

If(x + 1) is a factor of polynomial `p(x) = x^3-x^2-(2+sqrt2)x+sqrt2`, then p(−1) must be zero, as a result (x + 1) is not a factor of this polynomial.

`p(-1) = (-1)^3 - (-1)^2 - (2+sqrt2)(-1) + sqrt2`

= `-1-1+2+sqrt2+sqrt2`

= `2sqrt2`

As p(−1) ≠ 0,

Therefore, (x + 1) is not a factor of this polynomial.