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

2 Answers
nightowl
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)#

Jim G.
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)#

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