# Thread: How do you solve this division

1. ## How do you solve this division

(16a^3-17a+10)/ (4a+5)

I have to solve this operation. I should have a quotient and remainder??

How do I solve this?
Thanks
Joanne

2. $\displaystyle 16 a^3 -17a+10 = (4a+5)(something)$

In order to get a term on the left like $\displaystyle 16 a^3$ the $\displaystyle 4a$ has to multiply $\displaystyle 4a^2$, so let's try:

$\displaystyle 16 a^3 -17a+10 = (4a+5)(4a^2+something)$

Unfortunately now the right hand side (RHS) is:
$\displaystyle 16 a^3 +20a^2+something$

We don't want the $\displaystyle 20a^2$. So let's modify the 'something'. We have to multiply the $\displaystyle 4a$ by $\displaystyle -5a$ to get a $\displaystyle -20a^2$.

So the equation is now

$\displaystyle 16 a^3 -17a+10 = (4a+5)(4a^2-5a+something)$

We've added an $\displaystyle a^2$ term and an $\displaystyle a$ term. The last term to add is a constant term.

Can you find the last constant in the right hand side? Whatever is left over is the remainder in your division.