Question

The quotient of (x^4+5x^3-3x-15) and a polynomial is (x^3-3). What is the polynomial?

Answer 1

x+5

Explanation:

Edge 2020

Answer 2

Let f(x) be the required polynomial.

Then,
`(x^(4)+5x^(3)-3x-15)/(f(x)) =x^(3) -3`

Or,
`f(x) = (x^(4)+15x^(3)-3x-15)/(x^(3)-3 )`

Consider the numerator.

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

`=(x^(3)- 3)(x+5)`

Therefore,
`(x^(4)+5x^(3)-3x-15)/(x^(3)-3 )`

=
`((x^(3)-3)(x+5) )/(x^(3)-3 )`

= x + 5