How do you divide #( 2x^3-5x^2+22x)/(2x +3)#?

1 Answer
Jim G.
Mar 29, 2018

#x^2-4x+17-51/(2x+3)#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(2x+3)color(magenta)(-3x^2)-5x^2+22x#

#=color(red)(x^2)(2x+3)color(red)(-4x)(2x+3)color(magenta)(+12x)+22x#

#=color(red)(x^2)(2x+3)color(red)(-4x)(2x+3)color(red)(+17)(2x+3)color(magenta)(-51)#

#"quotient "=color(red)(x^2-4x+17)," remainder "=-51#

#rArr(2x^3-5x^2+22x)/(2x+3)#

#=x^2-4x+17-51/(2x+3)#

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