Question

Divide $x^3+7x^2+12x$ by $x^2+3x$.

• A. $x^2+3$
• B. $x^2+4$
• C. $x+3$
• D. $x+4$

Answer 1

The correct option is D $x+4$

We need to divide $x^3+7x^2+12x$ by $x^2+3x$.

First, let's factorize $x^3+7x^2+12x$.
Taking $x$ common from all the three terms:
$x^3+7x^2+12x$
$=x(x^2+7x+12)$
Splitting the middle term:
$=x(x^2\underset{–}{+7x}+12)$

$=x(x^2+4x+3x+12)$
Taking $x$ common from the first two terms and $3$ common from the last two terms:
$=x\left(x\right(x+4)+3(x+4\left)\right)$
$=x(x+4)(x+3)$

Now, let's factorize $x^2+3x$.
Taking $x$ common from the first two terms:
$x^2+3x=x(x+3)$


Now, let's divide $x^3+7x^2+12x$ by $x^2+3x$:
$\frac{x^3+7x^2+12x}{x^2+3x}$

$=\frac{x(x+4)(x+3)}{x(x+3)}$

The factors of $x$ and $x+3$ can be cancelled from the Numerator and Denominator and we are left with:
$=(x+4)$

The value obtained when $x^3+7x^2+12x$ is divided by $x^2+3x$ is equal to $x+4$.

Therefore, option (d.) is the correct answer.