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.
Feb 22, 2018
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
=x^2+8x+19+65/(x-3)