Given equation is [tex]\frac{{5x^{2}}+10x-15}{x+5}[/tex]
Solution:
We will divide the leading coefficients of the numerator and divisor
= [tex]\frac{5x^{2}}{x}=5x[/tex] so, quotient is 5x
Multiplying divisor x+5 by 5x we have [tex]5x^{2}+25x[/tex]
We will now subtract [tex]5x^{2}+25x[/tex] from [tex]5x^{2}+10x-15[/tex] and we get the new remainder as [tex]-15x-15[/tex]
[tex]\frac{{5x^{2}}+10x-15}{x+5}[/tex] becomes [tex]5x+\frac{-15x-15}{x+5}[/tex]
Now again divide the leading coefficient of numerator with x
[tex]\frac{-15x}{x}=-15[/tex] new quotient is -15.
Now multiplying x+5 by -15 =[tex]-15x-75[/tex]
We will subtract this [tex]-15x-75[/tex] from -15x-15 to get a new remainder
Now remainder becomes 60
So, [tex]\frac{-15x-15}{x+5}=-15+\frac{60}{x+5}[/tex]
The new equation becomes = [tex]5x-15+\frac{60}{x+5}[/tex]
The remainder is 60.
