How do you divide (3x^3 - 2x^2 - 12x - 2)/(x-7)?

1 Answer
Jim G.
Jun 2, 2017

3x^2+19x+121+845/(x-7)

Explanation:

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

"consider the numerator"

color(red)(3x^2)(x-7)color(magenta)(+21x^2)-2x^2-12x-2

=color(red)(3x^2)(x-7)color(red)(+19x)(x-7)color(magenta)(+133x)-12x-2

=color(red)(3x^2)(x-7)color(red)(+19x)(x-7)color(red)(+121)(x-7)color(magenta)(+847)-2

=color(red)(3x^2)(x-7)color(red)(+19x)(x-7)color(red)(+121)(x-7)+845

"quotient "=color(red)(3x^2+19x+121),"remainder "=845

rArr(3x^3-2x^2-12x-2)/(x-7)=3x^2+19x+121+845/(x-7)

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