Question

1. what is the quotient represented by the expression (\frac{5x^2 - 15x - 20}{5x + 5}) for all values of (a) where the expression is defined?

a. (x + 4)
b. (x - 4)
c. (2x - 4)
d. (2x + 4)

Explanation:

Step1: Factor numerator

Factor $5x^2-15x-20$. First factor out 5:
$5(x^2-3x-4)$
Then factor the quadratic:
$5(x-4)(x+1)$

Step2: Factor denominator

Factor $5x+5$. Factor out 5:
$5(x+1)$

Step3: Cancel common factors

Cancel $5(x+1)$ from numerator and denominator (valid for $x
eq -1$, where the original expression is defined):
$\frac{5(x-4)(x+1)}{5(x+1)} = x-4$

Answer:

b. $x - 4$