Question

100 POINTS PLEASE HELP (x^3 − 11x^2+ 22x + 40) ÷ (x − 5) Please solve this equation using the synthetic division method and show all steps

Answer 1

`(x^3-11x^2+ 22x + 40)/ (x-5)=(x^2-6x-8)`

Explanation:

When dividing
`(x^3-11x^2+ 22x + 40)` by
`(x-5),`

1. Multiply
`(x-5)` by
`x^2` and subtract the result from
`(x^3-11x^2+ 22x + 40)` to eliminate
`x^3:`

`(x^3-11x^2+ 22x + 40)-x^2(x-5)\\ \\=x^3-11x^2+22x+40-x^2+5x^2\\ \\=-6x^2+22x+40`

2. Multiply
`(x-5)` by
`-6x` and subtract the result from
`-6x^2+22x+40` to eliminate
`-6x^2:`

`-6x^2+22x+40-(-6x)(x-5)\\ \\=-6x^2+22x+40+6x^2-30x\\ \\=-8x+40`

3. Multiply
`(x-5)` by
`-8` and subtract the result from
`-8x+40` to eliminate
`-8x:`

`-8x+40-(-8)(x-5)\\ \\=-8x+40+8x-40\\ \\=0`

So,

`(x^3-11x^2+ 22x + 40)/ (x-5)=(x^2-6x-8)`