Question

NEEEED HELPPP NOWWWW Use long division to find the quotient below.
(x^5+ 18x^2 - 27x) - (x+3)

Answer 1

`{x}^(4) - 3 {x}^(3) + 9 {x}^(2) - 9x`

Option A is the correct option.

Explanation:

`\frac{ {x}^(5) + 18 {x}^(2) - 27x }{x + 3}`

Factor out X from the expression

`\frac{x( {x}^(4) + 18x - 27)}{x + 3}`

Add and subtract
`3 {x}^(3)`

`\frac{x( {x}^(4) + 3 {x}^(3) - 3 {x}^(3) + 18x - 27)}{x + 3}`

Write 18x as a difference

`\frac{x( {x}^(4) + 3 {x}^(3) - 3 {x}^(3) - 9 {x}^(2) + 9 {x}^(2) + 27x - 9x - 27 }{x + 3}`

factor out
`{x}^(3)`from the expression

`\frac{x( {x}^(3) (x + 3) - 3 {x}^(3) - 9 {x}^(2) + 9 {x}^(2) + 27x - 9x - 27) }{x + 3}`

Factor out
`- 3 {x}^(2)` from the expression

`\frac{x( {x}^(3) (x + 3) - 3 {x}^(2)(x + 3) + 9 {x}^(2) + 27x - 9x - 27) }{x + 3}`

factor out 9x from the expression

`\frac{x( {x}^(3)(x + 3) - 3 {x}^(2) (x + 3) + 9x(x + 3) - 9x - 27 }{x + 3}`

Factor out -9 from the expression

`\frac{x( {x}^(3) (x + 3) - 3 {x}^(2) (x + 3) + 9x(x + 3) - 9(x + 3)}{x + 3}`

factor out x+3 from the expression

`\frac{x(x + 3)( {x}^(3) - 3 {x}^(2) + 9x - 9) }{x + 3}`

Reduce the fraction with X+3

`x( {x}^(3) - 3 {x}^(2) + 9x - 9)`

Distribute X through the parentheses

`{x}^(4) - 3 {x}^(3) + 9 {x}^(2) - 9x`

hope this helps...

Good luck on your assignment...