Question

question 5 of 6
select the correct answer.
what is the quotient?
\\(\frac{-x^2 - 10x - 16}{(x + 2)(x + 4)}\\)
\\(\frac{-x + 8}{x + 4}\\)
\\(\frac{x + 2}{x + 4}\\)
\\(\frac{-(x + 8)}{x + 4}\\)
\\(\frac{-(x + 8)}{x + 2}\\)

Explanation:

Step1: Factor the numerator

First, factor out a negative sign from the numerator: $-x^2 - 10x - 16 = -(x^2 + 10x + 16)$. Then, factor the quadratic expression $x^2 + 10x + 16$. We need two numbers that multiply to 16 and add to 10, which are 2 and 8. So, $x^2 + 10x + 16 = (x + 2)(x + 8)$. Thus, the numerator becomes $-(x + 2)(x + 8)$.

Step2: Simplify the fraction

Now, the original expression is $\frac{-(x + 2)(x + 8)}{(x + 2)(x + 4)}$. We can cancel out the common factor $(x + 2)$ from the numerator and the denominator (assuming $x
eq -2$). After canceling, we get $\frac{-(x + 8)}{x + 4}$.

Answer:

$\frac{-(x + 8)}{x + 4}$ (corresponding to the option $\boldsymbol{\frac{-(x + 8)}{x + 4}}$)