Question

Find the quotient when $x^3+x^2+x+1$ is divided by $x+1$.

• A. $x+1$
• B. $x^2+1$
• C. $x-1$
• D. $x^2-1$

Answer 1

The correct option is B $x^2+1$

We need to divide $x^3+x^2+x+1$ by $x+1$.

First, we need to factorize $x^3+x^2+x+1$

Taking $x^2$ common from the first two terms and $1$ common from the last two terms:
$x^3+x^2+x+1=x^2(x+1)+1(x+1)$
$=(x+1)(x^2+1)$

Now, we can easily divide $x^3+x^2+x+1$ by $x+1$:
$\frac{x^3+x^2+x+1}{x+1}$
$=\frac{(x+1)(x^2+1)}{(x+1)}$
$=x^2+1$

The quotient when $x^3+x^2+x+1$ divided by $x+1$ would be $x^2+1$.
Therefore, option (b.) is the correct answer.