Question

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

Answer 1

The missing polynomial must be of degree 1, since the dividend has degree 4 and the divisor has degree 3. So we're looking for a polynomial
`ax+b` such that

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

Expanding the left hand side gives

`ax^4+bx^3-3ax-3b`

We need to have

so that the missing polynomial is
`\boxed{x+5}`.