How do you evaluate #(x ^ { 3} + 3x ^ { 2} - 6x + 7) \div ( x + 4)#?
1 Answer
Jan 2, 2018
Explanation:
#"use the divisor as a factor in the numerator"#
#"consider the numerator"#
#color(red)(x^2)(x+4)color(magenta)(-4x^2)+3x^2-6x+7#
#=color(red)(x^2)(x+4)color(red)(-x)(x+4)color(magenta)(+4x)-6x+7#
#=color(red)(x^2)(x+4)color(red)(-x)(x+4)color(red)(-2)(x+4)color(magenta)(+8)+7#
#=color(red)(x^2)(x+4)color(red)(-x)(x+4)color(red)(-2)(x+4)+15#
#"quotient "=color(red)(x^2-x-2)," remainder "=15#
#rArr(x^3+3x^2-6x+7)/(x+4)#
#=x^2-x-2+15/(x+4)#