The quotient of (x⁴ + 5x³ - 3x - 15) divided by a polynomial is (x³ - 3). What is the polynomial?

Solution:

Given polynomial (x⁴ + 5x³ - 3x - 15). Let it be f(x)

Quotient is (x³ - 3). Let it be q(x)

The divisor p(x) and the remainder r(x) can be obtained by long division of the polynomial f(x) by q(x)

f(x) = p(x) × q(x)  + r(x)

Hence, the required polynomial is x + 5

The quotient of (x⁴ + 5x³ - 3x - 15) divided by a polynomial is (x³ - 3). What is the polynomial?

Summary:

The quotient of (x⁴ + 5x³ - 3x - 15) divided by a polynomial is (x³ - 3). The required polynomial is x + 5.