Question 936797
Polynomial Division works the same way as base-ten long-division.  The powers of x are used instead of place value powers of 10.


How many times does x go into x^2?
{{{x^2/x=x}}}
Show x above the first term of the dividend.


________________________x
________________________________________________
________________|
____x+3_________)______x^2______-7x________+10



Multiply and then subtract....


________________________x
________________________________________________
________________|
____x+3_________)______x^2______-7x________+10
_______________________x^2______3x
__________________________________
_______________________0_______-10x



Bring down the next term, and continue the process...


________________________x________-10
________________________________________________
________________|
____x+3_________)______x^2______-7x________+10
_______________________x^2______3x
__________________________________
_______________________0_______-10x________10
_______________________________-10x________-30
_________________________________________________
________________________________0__________40



The degree of the remainder is less than the degree of the divisor, so the quotient found is  {{{highlight(x-10+40/(x+3))}}}