How do you evaluate #(x ^ { 3} + 3x ^ { 2} - 6x + 7) \div ( x + 4)#?

1 Answer
Jim G.
Jan 2, 2018

#x^2-x-2+15/(x+4)#

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)#

Related questions
Impact of this question
600 views around the world
You can reuse this answer
Creative Commons License