How do you divide (5x ^ { 3} + 9x ^ { 2} - 26x - 27) \div ( x + 3)?

2 Answers
Jul 27, 2017

7

Explanation:

Use the Factor Theorem, f(a)=0

x+3=0
x=-3

f(-3)=5x^3+9x^2-26x-27
=5(-3)^3+9(-3)^2-26(-3)-27
=7

Jul 27, 2017

5x^2-6x-8-3/(x+3)

Explanation:

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

"consider the numerator"

color(red)(5x^2)(x+3)color(magenta)(-15x^2)+9x^2-26x-27

=color(red)(5x^2)(x+3)color(red)(-6x)(x+3)color(magenta)(+18x)-26x-27

=color(red)(5x^2)(x+3)color(red)(-6x)(x+3)color(red)(-8)(x+3)color(magenta)(+24)-27

=color(red)(5x^2)(x+3)color(red)(-6x)(x+3)color(red)(-8)(x+3)-3

"quotient "=color(red)(5x^2-6x-8)," remainder "=-3

rArr(5x^3+9x^2-26x-27)/(x+3)

=5x^2-6x-8-3/(x+3)