How do you divide (-x^3+13x^2-x-5)/(x-4)−x3+13x2−x−5x−4?
2 Answers
Explanation:
One way is to use the divisor as a factor in the numerator.
color(magenta)"add / subtract "" the terms that occur as a consequence"add / subtract the terms that occur as a consequence
"consider the numerator"consider the numerator
color(red)(-x^2)(x-4)color(magenta)(-4x^2)+13x^2-x-5−x2(x−4)−4x2+13x2−x−5
=color(red)(-x^2)(x-4)color(red)(+9x)(x-4)color(magenta)(+36x)-x-5=−x2(x−4)+9x(x−4)+36x−x−5
=color(red)(-x^2)(x-4)color(red)(+9x)(x-4)color(red)(+35)(x-4)color(magenta)(+140)-5=−x2(x−4)+9x(x−4)+35(x−4)+140−5
rArr"quotient "=color(red)(-x^2+9x+35)" remainder "=135⇒quotient =−x2+9x+35 remainder =135
Explanation:
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!
