Q9. - Algebra 1

Question

MULTIPLE CHOICE The area of a rectangle is $x^2+5x+6$ square feet. If the width is $x+2$, what is the length of the rectangle.

1. $x+2$
   
2. $x+3$
   
3. 1
4. 3

Step-by-Step Solution

Answer

The length of the rectangle is $\left(x+3\right)$.

Step 1. Factor.

Factor the given polynomial.

$$\begin{gathered} x^2+5x+6=x^2+3x+2x+6 \\ =x\left(x+3\right)+2\left(x+3\right) \end{gathered}$$

Step 2. Simplify.

Simplify the obtained expression.

$\left(x+2\right)\left(x+3\right)$

Step 3. Write the conclusion.

The area of rectangle is given by $A=l\cdot b$. By comparing the equation of area to obtained expression, the length of the rectangle is $\left(x+3\right)$. Option B completely matches with the obtained equation therefore, option B is the required answer.