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

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

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

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

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

So the equation is now

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

We've added an $a^2$ term and an $a$ 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.