How do you divide #(4x^3 -12x^2+5x+3)/((x +3) )#?

2 Answers
Robert C.
Feb 9, 2018

#4x^2 - 24x + 77, R -228#

Explanation:

polynomial long division - yay!

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Jim G.
Feb 10, 2018

#4x^2-24x+77-228/(x+3)#

Explanation:

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

#"consider the numerator"#

#color(red)(4x^2)(x+3)color(magenta)(-12x^2)-12x^2+5x+3#

#=color(red)(4x^2)(x+3)color(red)(-24x)(x+3)color(magenta)(+72x)+5x+3#

#=color(red)(4x^2)(x+3)color(red)(-24x)(x+3)color(red)(+77)(x+3)color(magenta)(-231)+3#

#=color(red)(4x^2)(x+3)color(red)(-24x)(x+3)color(red)(+77)(x+3)-228#

#"quotient "=color(red)(4x^2-24x+77)," remainder "=-228#

#rArr(4x^3-12x^2+5x+3)/(x+3)#

#=4x^2-24x+77-228/(x+3)#

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