Question

How do you divide `(x^3-7x-6) / (x+1)`?

Answer 1

The quotient is `=x^2-x-6` and the remainder is `=0`

Explanation:

Perform a long division

`color(white)(aaaa)` `x^3+0x^2-7x-6` `color(white)(aaaa)` `|` `x+1`

`color(white)(aaaa)` `x^3+x^2` `color(white)(aaaaaaaaaaaaa)` `|` `x^2-x-6`

`color(white)(aaaaa)` `0-x^2-7x`

`color(white)(aaaaaaa)` `-x^2-x`

`color(white)(aaaaaaa)` `-0-6x-6`

`color(white)(aaaaaaaaaaa)` `-6x-6`

`color(white)(aaaaaaaaaaaa)` `-0-0`

The quotient is `=x^2-x-6` and the remainder is `=0`

`(x^3+0x^2-7x-6)/(x+1)=x^2-x-6`

Answer 2

`x^2-x-6`

Explanation:

Given: `(x^3-7x-6)/(x+1)`

Using place keepers of no value. Example: `0x^2`

`color(white)("ddddd.ddddd.d")x^3+0x^2-7x-6`
`color(red)(+x^2)(x+1) ->ul(x^3+x^2 larr" Subtract")`
`color(white)("dddddddddddd.")0 -x^2-7x-6`
`color(red)(-x)(x+1)->color(white)("dd.")ul(-x^2-x larr" Subtract")`
`color(white)("dddddddddddddddd")0-6x-6`
`color(red)(-6)(x+1)->color(white)("dddddd.")ul(-6x-6larr" Subtract")`
`color(white)("dddddddddddddddddddd")0+0 larr" Remainder"`

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`(x^3-7x-6)/(x+1)=color(red)(x^2-x-6)`