How do you divide #(-x^3+13x^2-x-5)/(x-4)#?
One way is to use the divisor as a factor in the numerator.
#color(magenta)"add / subtract "" the terms that occur as a consequence"#
#"consider the numerator"#
#rArr"quotient "=color(red)(-x^2+9x+35)" remainder "=135#
For this question, use synthetic division (if you don't know what that is, check this out: http://www.purplemath.com/modules/synthdiv.htm)
x-4 is linear, so we are allowed to use synthetic division.
Your synthetic division should look something like this:
4| -1 13 -1 -5
-4 36 140 -1 9 35 135
So we get that
Alternatively, you can use the long division to do this, though it will take a bit longer (https://www.mathsisfun.com/algebra/polynomials-division-long.html)
Hope that helps!