How do you solve (x^ { 3} - 4x ^ { 2} - 11x + 30 )\div (x - 2)?(x3−4x2−11x+30)÷(x−2)?

2 Answers
sankarankalyanam
Jan 29, 2018

color(green)(x^2 -2x -15)x2−2x−15

Explanation:

color(white)(aaaa)2color(white)(aa)|color(white)(aa)1color(white)(aa)-4color(white)(aa)-11color(white)(aa)30aaaa2aa∣aa1aa−4aa−11aa30

color(white)(aaaaaaaaaa)darrcolor(white)(aaaa)2color(white)(aa)-4color(white)()-30aaaaaaaaaa↓aaaa2aa−4−30

color(white)(aaaaaaa)---------aaaaaaa−−−−−−−−−

color(white)(aaaaaaaaaaa)1color(white)(aa)-2color(white)(aa)-15color(white)(aa)0aaaaaaaaaaa1aa−2aa−15aa0

x^2 -2x -15x2−2x−15

Jim G.
Jan 29, 2018

x^2-2x-15x2−2x−15

Explanation:

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

"consider the numerator"consider the numerator

color(red)(x^2)(x-2)color(magenta)(+2x^2)-4x^2-11x+30x2(x−2)+2x2−4x2−11x+30

=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(magenta)(-4x)-11x+30=x2(x−2)−2x(x−2)−4x−11x+30

=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(red)(-15)(x-2)color(magenta)(-30)+30=x2(x−2)−2x(x−2)−15(x−2)−30+30

=color(red)(x^2)(x-2)color(red)(-2x)(x-2)color(red)(-15)(x-2)+0=x2(x−2)−2x(x−2)−15(x−2)+0

"quotient "=color(red)(x^2-2x-15)," remainder" =0quotient =x2−2x−15, remainder=0

rArr(x^3-4x^2-11x+30)/(x-2)=x^2-2x-15⇒x3−4x2−11x+30x−2=x2−2x−15

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