How to divide the first expression by the second? : 1) #2x^3-7x^2+15x-3, x-3#

1 Answer
Jim G.
Jan 18, 2018

#2x^2-x+12+33/(x-3)#

Explanation:

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

#"consider the numerator"#

#color(red)(2x^2)(x-3)color(magenta)(+6x^2)-7x^2+15x-3#

#=color(red)(2x^2)(x-3)color(red)(-x)(x-3)color(magenta)(-3x)+15x-3#

#=color(red)(2x^2)(x-3)color(red)(-x)(x-3)color(red)(+12)(x-3)color(magenta)(+36)-3#

#color(red)(2x^2)(x-3)color(red)(-x)(x-3)color(red)(+12)(x-3)+33#

#"quotient "=color(red)(2x^2-x+12)," remainder "=33#

#rArr(2x^3-7x^2+15x-3)/(x-3)#

#=2x^2-x+12+33/(x-3)#

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