Question

Please i really need help on this one please!!!! :( I need an answer ASAP

Answer 1

We want to multiply $\displaystyle{ \frac{r^2+7r+10}{3}$ by $\displaystyle{ \frac{3r-30}{r^2-5r-50}$, and simplify.

The first thing we do in this type of problems, is factorize as much as possible, and see what cancels out. 

$\displaystyle{ r^2+7r+10$ can be factored into (r+2)(r+5) as 2 and 5 are two numbers whose sum is 7, and product is 10.

Similarly $\displaystyle{ r^2-5r-50$ can be factoredinto (r-10)(r+5) as -10 and 5 are two numbers whose sum is -5, and product is -50.

Last, (3r-30) can be factored as 3(r-10). 

Thus the product is equal to:

$\displaystyle{ \frac{(r+2)(r+5)}{3}\cdot \frac{3(r-10)}{(r-10)(r+5)}$, 

so canceling all equal terms in the numerator and denominator we are left with 
                                         r+2.


Answer: A) r+2