When a certain polynomial is divided by x  3, its quotient is x2  5x  7 and its remainder is 5. What is the polynomial? (hint: use the division statement!)

Answer 1

The division statement can be written as:

Polynomial = Divisor * Quotient + Remainder

Since the divisor is (x - 3), the polynomial can be expressed as:

Polynomial = (x - 3) * (x^2 - 5x - 7) + 5

We can now multiply the divisor and quotient:

Polynomial = x * (x^2 - 5x - 7) - 3 * (x^2 - 5x - 7) + 5

Simplifying, we get:

Polynomial = x^3 - 5x^2 - 7x - 3x^2 + 15x + 21 + 5

Combining like terms, the polynomial is:

Polynomial = x^3 - 8x^2 + 8x + 26