How to divide the first expression by the second? : 1) 2x^3-7x^2+15x-3, x-3

1 Answer
Jan 18, 2018

2x^2-x+12+33/(x-3)

Explanation:

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

"consider the numerator"

color(red)(2x^2)(x-3)color(magenta)(+6x^2)-7x^2+15x-3

=color(red)(2x^2)(x-3)color(red)(-x)(x-3)color(magenta)(-3x)+15x-3

=color(red)(2x^2)(x-3)color(red)(-x)(x-3)color(red)(+12)(x-3)color(magenta)(+36)-3

color(red)(2x^2)(x-3)color(red)(-x)(x-3)color(red)(+12)(x-3)+33

"quotient "=color(red)(2x^2-x+12)," remainder "=33

rArr(2x^3-7x^2+15x-3)/(x-3)

=2x^2-x+12+33/(x-3)