Question

Divide $p\left(x\right)$ by $g\left(x\right)$ in the following case and verify division algorithm
$p\left(x\right)=x^2+4x+4;g\left(x\right)=x+2$

Answer 1

The division of $p\left(x\right)=x^2+4x+4$ by $g\left(x\right)=x+2$ is as shown above:

Now we know that the division algorithm states that:

Dividend$=($Divisor$\times$quotient$)+$Remainder

Here, the dividend is $x^2+4x+4$, the divisor is $x+2$, the quotient is $x+2$ and the remainder is $0$, therefore,

$x^2+4x+4=\left[\right(x+2\left)\right(x+2\left)\right]+0\Rightarrow x^2+4x+4=\left[x\right(x+2)+2(x+2\left)\right]\Rightarrow x^2+4x+4=x^2+2x+2x+4\Rightarrow x^2+4x+4=x^2+4x+4$

Hence, the division algorithm is verified.