Question

How do you find the quotient of (x^3+6x^2-x-30) divided by (x^2+8x+15)?

Answer 1

Quotient is `x-2`

Explanation:

`x^3+6x^2-x-30`

=`x^3+8x^2+15x-2x^2-16x-30`

=`x*(x^2+8x+15)-2*(x^2+8x+15)`

=`(x^2+8x+15)*(x-2)`

Hence quotient is `x-2`

Answer 2

`(x^3-6x^2-x-30)div(x^2+8x+15)=color(blue)(x-2)`

Explanation:

It is possible to solve this by factoring but factoring cubic equations can be time consuming.
As an alternative, I would suggest using simple polynomial long division.

`color(white)("XXXXXXXXX")ul(color(white)("xx")xcolor(white)("x")-2color(white)("xxxxxxxxxxxxx"))`
`x^2+8x+15" ) "x^3color(white)("x")+6x^2color(white)("x")-xcolor(white)("x")-30`
`color(white)("XXXXXXXXXx")ul(x^3color(white)("x")+8x^2+15x)`
`color(white)("XXXXXXXXXxxxx")-2x^x-16xcolor(white)("x")-30`
`color(white)("XXXXXXXXXxxxx")ul(-2x^x-16xcolor(white)("x")-30)`