Question

Find the factors of $x^3+2x^2+2x+1$

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

Answer 1

Answer: (A), (B)

$(x^2+x+1)$

Let $p\left(x\right)=(x^3+2x^2+2x+1)$ be the given polynomial
By observation, we can see that by putting
$x=-1,p\left(x\right)=0$
$\therefore x=-1$ is the root of $p\left(x\right)$
$\Rightarrow (x+1)$ is a factor of $p\left(x\right)$

To find the other factor, we perform long division of $p\left(x\right)$ by $(x+1)$

$\therefore$ The two factors of $p\left(x\right)$ are $(x+1)$ and $(x^2+x+1)$