Answer:
Step-by-step explanation:
[tex] \frac{2 {x}^{3} + 9 {x}^{2} + x - 12}{x + 4} [/tex]
Write [tex]9 {x}^{2} [/tex] as a sum
[tex] \frac{2 {x}^{3} - 2 {x}^{2} + 11 {x}^{2} + x - 12}{x + 4} [/tex]
Write X as a sum
[tex] \frac{2 {x}^{3} - 2 {x}^{2} + 11 {x}^{2} - 11x + 12x - 12 }{x + 4} [/tex]
Factor out [tex]2 {x}^{2} [/tex] from the expression
[tex] \frac{2 {x}^{2}(x - 1) + 11 {x}^{2} - 11x + 12x - 12 }{x + 4} [/tex]
Factor out 11x from the expression
[tex] \frac{2 {x}^{2} (x - 1) + 11x(x - 1) + 12x - 12}{x + 4} [/tex]
Factor out 12 from the expression
[tex] \frac{2 {x}^{2}(x - 1) + 11(x - 1) + 12(x - 1) }{x + 4} [/tex]
Factor out X - 1 from the expression
[tex] \frac{(x - 1)(2 {x}^{2} + 11x + 12)}{x + 4} [/tex]
Write 11x as a sum
[tex] \frac{(x - 1)(2 {x}^{2} + 8x + 3x + 12)}{x + 4} [/tex]
Factor out 2x from the expression
[tex] \frac{(x - 1)(2x(x + 4) + 3x + 12)}{x + 4} [/tex]
Factor out 3 from the expression
[tex] \frac{(x - 1)(2x(x + 4) + 3(x + 4)}{x + 4} [/tex]
Factor out X + 4 from the expression
[tex] \frac{(x - 1)(x + 4)(2x + 3)}{x + 4} [/tex]
Reduce the fraction with X + 4
[tex](x - 1)(2x + 3)[/tex]
Multiply the parantheses
[tex]2 {x}^{2} + 3x - 2x - 3[/tex]
Collect like terms
[tex]2 {x}^{2} + x - 3[/tex]
Hope this helps...
Good luck on your assignment...
