Question

the area (in square inches) of a rectangle is given by the polynomial function $a(q)=q^{2}+9q + 18$. if the length of the rectangle is $(q + 6)$ inches, what is the width?
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| inches

Explanation:

Step1: Recall area formula

The area of a rectangle is $A = l\times w$, where $A$ is area, $l$ is length and $w$ is width. Given $A(q)=q^{2}+9q + 18$ and $l=(q + 6)$, we need to find $w=\frac{A}{l}$.

Step2: Factor the area polynomial

Factor $q^{2}+9q + 18$. We need two numbers that multiply to $18$ and add up to $9$. The numbers are $6$ and $3$, so $q^{2}+9q + 18=(q + 6)(q+3)$.

Step3: Calculate the width

Since $w=\frac{A}{l}$, substituting $A=(q + 6)(q + 3)$ and $l=(q + 6)$, we get $w=\frac{(q + 6)(q + 3)}{q + 6}$. Canceling out the common factor $(q + 6)$ (assuming $q
eq - 6$), we find $w=(q + 3)$.

Answer:

$q + 3$