How do you divide (x^3-13x-18) / (x-4) x3−13x−18x−4?

1 Answer
Jim G.
Aug 8, 2017

x^2+4x+3-6/(x-4)x2+4x+3−6x−4

Explanation:

"one way is to use the divisor as a factor in the numerator"one way is to use the divisor as a factor in the numerator

"consider the numerator"consider the numerator

color(red)(x^2)(x-4)color(magenta)(+4x^2)-13x-18x2(x−4)+4x2−13x−18

=color(red)(x^2)(x-4)color(red)(+4x)(x-4)color(magenta)(+16x)-13x-18=x2(x−4)+4x(x−4)+16x−13x−18

=color(red)(x^2)(x-4)color(red)(+4x)(x-4)color(red)(+3)(x-4)color(magenta)(+12)-18=x2(x−4)+4x(x−4)+3(x−4)+12−18

=color(red)(x^2)(x-4)color(red)(+4x)(x-4)color(red)(+3)(x-4)-6=x2(x−4)+4x(x−4)+3(x−4)−6

"quotient "=color(red)(x^2+4x+3)," remainder "=-6quotient =x2+4x+3, remainder =−6

rArr(x^3-13x-18)/(x-4)=x^2+4x+3-6/(x-4)⇒x3−13x−18x−4=x2+4x+3−6x−4

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