Question

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

Answer 1

Answer:

$2 {x}^{2} + x - 3$

Step-by-step 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

$\frac{(x - 1)(2x(x + 4) + 3x + 12)}{x + 4}$

Factor out 3 from the expression

$\frac{(x - 1)(2x(x + 4) + 3(x + 4)}{x + 4}$

Factor out X + 4 from the expression

$\frac{(x - 1)(x + 4)(2x + 3)}{x + 4}$

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...