What is the quotient of #(3x^4-4x^2+8x-1)div(x-2)#?
1 Answer
Jul 5, 2017
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#