How do you divide #(x ^ { 3} + 9x ^ { 2} + 20x + 12) \div ( x + 2)#?

2 Answers
Jim G.
Jun 3, 2017

#x^2+7x+6#

Explanation:

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

#"consider the numerator"#

#color(red)(x^2)(x+2)color(magenta)(-2x^2)+9x^2+20x+12#

#=color(red)(x^2)(x+2)color(red)(+7x)(x+2)color(magenta)(-14x)+20x+12#

#=color(red)(x^2)(x+2)color(red)(+7x)(x+2)color(red)(+6)(x+2)color(magenta)(-12)+12#

#=color(red)(x^2)(x+2)color(red)(+7x)(x+2)color(red)(+6)(x+2)#

#"quotient "=color(red)(x^2+7x+6)," remainder "=0#

#rArr(x^3+9x^2+20x+12)/(x+2)=x^2+7x+6#

Barney V.
Jun 12, 2017

#color(blue)(x^2+7x+6#

Explanation:

#(x^3+9x^2+20x+12)-:(x+2)#

# color(white)(................)color(blue)(x^2+7x+6#
#color(white)(aa)x+2##|##overline(x^3+9x^2+20x+12)#
#color(white)(..............)ul(x^3+2x^2)#
#color(white)(........................)7x^2+20x#
#color(white)(........................)ul(7x^2+14x)#
#color(white)(...................................)6x+12#
#color(white)(...................................)ul(6x+12)#

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