How do you solve #(x^ { 3} - 4x ^ { 2} - 11x + 30 )\div (x - 2)?#

2 Answers
Jan 29, 2018

Answer:

#color(green)(x^2 -2x -15)#

Explanation:

#color(white)(aaaa)2color(white)(aa)|color(white)(aa)1color(white)(aa)-4color(white)(aa)-11color(white)(aa)30#

#color(white)(aaaaaaaaaa)darrcolor(white)(aaaa)2color(white)(aa)-4color(white)()-30#

#color(white)(aaaaaaa)---------#

#color(white)(aaaaaaaaaaa)1color(white)(aa)-2color(white)(aa)-15color(white)(aa)0#

#x^2 -2x -15#

Jan 29, 2018

Answer:

#x^2-2x-15#

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)-4x^2-11x+30#

#=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(magenta)(-4x)-11x+30#

#=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(red)(-15)(x-2)color(magenta)(-30)+30#

#=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(red)(-15)(x-2)+0#

#"quotient "=color(red)(x^2-2x-15)," remainder" =0#

#rArr(x^3-4x^2-11x+30)/(x-2)=x^2-2x-15#