Question

The quotient of (x5 – 3x3 – 3x2 – 10x 15) and a polynomial is (x2 – 5). what is the polynomial?

Answer 1

`x^3+2x-3`

Explanation:

the quotient of
`(x^5 - 3x^3 - 3x^2 - 10x+15)`and a polynomial is
`(x^2 -5)`

`(x^5 - 3x^3 - 3x^2 - 10x+15)/(x^2-5)`

WE use long division

`x^3+2x-3`

-------------------------------------------------

`(x^2-5)`
`x^5 - 0x^4-3x^3 - 3x^2 - 10x+15`

`x^5 +0x^4 -5x^3`

--------------------------------------------------(subtract)

`2x^3 - 3x^2-10x`

`2x^3 + 0x^2 -10x`

------------------------------------------------------(subtract)

`-3x^2+0x+15`

`-3x^2+ 0x +15`

-----------------------------------------------------(subtract)

0

Answer 2

x^3 + 2x - 3

Just divide x^5-3x^3-3x^2-10x+15 by the quotient and you get the polynomial searched.