What is the quotient of #(3x^4-4x^2+8x-1)div(x-2)#?

1 Answer
Jim G.
Jul 5, 2017

#3x^3+6x^2+8x+24#

Explanation:

One way of dividing is to use the divisor as a factor in the numerator.

#"consider the numerator"#

#color(red)(3x^3)(x-2)color(magenta)(+6x^3)-4x^2+8x-1#

#=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(magenta)(+12x^2)-4x^2+8x-1#

#=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(magenta)(+16x)+8x-1#

#=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(red)(+24)(x-2)color(magenta)(+48)-1#

#=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(red)(+24)(x-2)+47#

#rArr"quotient "=color(red)(3x^3+6x^2+8x+24)#

#"remainder "=47#

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