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)#