Question

Determine which of the following polynomials has $(x+1)$factor:

a) $x^3+x^2+x+1$

b) $x^4+x^3+x^2+x+1$

Answer 1

Part (A).

Let $x+1=0$

Then, $x=-1$ Put the given polynomial

We get,

$x^3+x^2+x+1$

${(-1)}^3+{(-1)}^2+(-1)+1$

$-1+1-1+1=0$

Hence , this is a factor of $x+1$.

Part (B).

Let $x+1=0$

Then, $x=-1$ Put the given polynomial

We get,

$x^4+x^3+x^2+x+1$

${(-1)}^4+{(-1)}^3+{(-1)}^2+(-1)+1$

$1-1+1-1+1=1$

Hence , this is a no factor of $x+1$.