(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
$\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.