Question

the length of a rectangle is 3x + 2. its area is 21x^2 - x - 10. to find an expression that represents the width of the rectangle, perform the following operation(s) and simplify completely. $\frac{21x^{2}-x - 10}{3x + 2}$ (1 point)

Explanation:

Step1: Factor the numerator

We factor $21x^{2}-x - 10$.
We need to find two numbers that multiply to $21\times(- 10)=-210$ and add up to $-1$. The numbers are $-15$ and $14$.
So, $21x^{2}-x - 10=21x^{2}+14x-15x - 10=7x(3x + 2)-5(3x + 2)=(3x + 2)(7x-5)$.

Step2: Simplify the fraction

We have the fraction $\frac{21x^{2}-x - 10}{3x + 2}$. Substituting the factored - form of the numerator, we get $\frac{(3x + 2)(7x-5)}{3x + 2}$.
Cancel out the common factor $(3x + 2)$ in the numerator and the denominator.
The simplified expression is $7x-5$.

Answer:

$7x - 5$