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

NEEEED HELPPP NOWWWW Use long division to find the quotient below. (x^5+ 18x^2 - 27x-example-1

1 Answer

4 votes

Answer:


{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...

User Yimin Rong
by
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