Question

How do you divide `(x ^ { 3} + 7x ^ { 2} + 7x - 15) \div ( x + 3)`?

Answer 1

`x^2+4x-5`

Explanation:

Answer 2

`x^2+4x-5`

Explanation:

`"one way is to use the divisor as a factor in the numerator"`

`"consider the numerator"`

`color(red)(x^2)(x+3)color(magenta)(-3x^2)+7x^2+7x-15`

`=color(red)(x^2)(x+3)color(red)(+4x)(x+3)color(magenta)(-12x)+7x-15`

`=color(red)(x^2)(x+3)color(red)(+4x)(x+3)color(red)(-5)(x+3)cancel(color(magenta)(+15))cancel(-15)`

`rArr"quotient "=color(red)(x^2+4x-5)," remainder "=0`

`rArr(x^3+7x^2+7x-15)/(x+3)=x^2+4x-5`

Answer 3

`(x^3+7x^2+7x-15)-: (x+3) =x^2+4x-5`

Explanation:

For the formatting for spacing I use hash color(white)("d") hash

Unfortunately the hash " " hash now fails more times than it works.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(white)("dddddddddd.") x^3+7x^2+7x-15`
`color(magenta)(x^2) (x+3) -> ul(x^3+3x^2 larr" Subtract" )`
`color(white)("dddddddddd.d")0+4x^2 +7x-15`
`color(magenta)(4x)(x+3)->color(white)("dddd") ul(4x^2+12x larr" Subtract")`
`color(white)("ddddddddddddddd.d")0-5x-15`
`color(magenta)(-5)(x+3)->color(white)("ddddddd")ul(-5x-15larr" Subtract")`
`color(white)("ddddddddddddddddddddd")0+0`

`(x^3+7x^2+7x-15)-: (x+3) =color(magenta)(x^2+4x-5)`