Question

What is the simplified form of the quantity 4 z squared plus 16z plus 15 over the quantity 2 z squared minus z minus 15?

Answer 1

Because both of those expressions are second degree polynomials, you are going to get a whole number with a remainder.  Since 2 goes into 4 twice, our whole number is 2.  If we do the multiplication and subsequent subtraction, we have a remainder of 18z + 45.  So our simplification, if you can call it that (it's really not that simple) is $2R \frac{18z+45}{2 z^{2}-z-15 }$