How do you simplify \frac { x ^ { 3} + 5x ^ { 2} - 5x + 8} { x - 3}?

2 Answers
Feb 22, 2018

Use long division to factorise the numerator

Explanation:

Using long division, we divide the numerator by the denominator to give ourselves a quadratic and a remainder.

(x^3+5x^2-5x)/(x-3) =(x^2+8x+19)+65/(x-3)

Feb 22, 2018

x^2+8x+19+65/(x-3)

Explanation:

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

"consider the numerator"

color(red)(x^2)(x-3)color(magenta)(+3x^2)+5x^2-5x+8

=color(red)(x^2)(x-3)color(red)(+8x)(x-3)color(magenta)(+24x)-5x+8

=color(red)(x^2)(x-3)color(red)(+8x)(x-3)color(red)(+19)(x-3)color(magenta)(+57)+8

=color(red)(x^2)(x-3)color(red)(+8x)(x-3)color(red)(+19)(x-3)+65

"quotient "=color(red)(x^2+8x+19)," remainder "=65

>rArr(x^3+5x^2-5x+8)/(x-3)

=x^2+8x+19+65/(x-3)