Question

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

Answer 1

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`

Answer 2

`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)`