How do you divide ( -3x^3+ 16x^2-24x+9 )/(x + 1 )?

2 Answers
Nov 19, 2017

-3x^3+16x^2-24x+9 is not divisible by x+1

Explanation:

If we descompose -3x^3+16x^2-24x+9 we obtain:
(x-3)(-3x^2+7x+3) which is not divisible by x+1.

Nov 19, 2017

-3x^2+19x-43+52/(x+1)

Explanation:

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

"consider the numerator"

color(red)(-3x^2)(x+1)color(magenta)(+3x^2)+16x^2-24x+9

=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(magenta)(-19x)-24x+9

=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(red)(-43)(x+1)color(magenta)(+43)+9

=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(red)(-43)(x+1)+52

"quotient "=color(red)(-3x^2+19x-43)," remainder "=52

rArr(-3x^3+16x^2-24x+9)/(x+1)

=-3x^2+19x-43+52/(x+1)