Question

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

Multiply r^2 + 7r + 10 / 3 by 3r - 30 / r^2 - 5r - 50

A. r + 2

B. 7r^2 - 20r - 300 / -5r - 5

C. (r + 5)( r + 2) / (r + 10)

D. 3r + 6 / 2

Answer 1

We want to multiply
`\displaystyle{ (r^2+7r+10)/(3)` by
`\displaystyle{ (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{ ((r+2)(r+5))/(3)\cdot (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