Question

(2x^3+9x^2+x-12)/(x+4) simplify

Answer 1

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

Explanation:

`\frac{2 {x}^(3) + 9 {x}^(2) + x - 12}{x + 4}`

Write
`9 {x}^(2)` as a sum

`\frac{2 {x}^(3) - 2 {x}^(2) + 11 {x}^(2) + x - 12}{x + 4}`

Write X as a sum

`\frac{2 {x}^(3) - 2 {x}^(2) + 11 {x}^(2) - 11x + 12x - 12 }{x + 4}`

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

`\frac{2 {x}^(2)(x - 1) + 11 {x}^(2) - 11x + 12x - 12 }{x + 4}`

Factor out 11x from the expression

`\frac{2 {x}^(2) (x - 1) + 11x(x - 1) + 12x - 12}{x + 4}`

Factor out 12 from the expression

`\frac{2 {x}^(2)(x - 1) + 11(x - 1) + 12(x - 1) }{x + 4}`

Factor out X - 1 from the expression

`\frac{(x - 1)(2 {x}^(2) + 11x + 12)}{x + 4}`

Write 11x as a sum

`\frac{(x - 1)(2 {x}^(2) + 8x + 3x + 12)}{x + 4}`

Factor out 2x from the expression

`((x - 1)(2x(x + 4) + 3x + 12))/(x + 4)`

Factor out 3 from the expression

`((x - 1)(2x(x + 4) + 3(x + 4))/(x + 4)`

Factor out X + 4 from the expression

`((x - 1)(x + 4)(2x + 3))/(x + 4)`

Reduce the fraction with X + 4

`(x - 1)(2x + 3)`

Multiply the parantheses

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

Collect like terms

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

Hope this helps...

Good luck on your assignment...