Answer:
(C) −5x^3 + x + 3.
Explanation:
To divide 15x^5 - 3x^3 - 9x^2 by -3x^2, we can follow these steps:
Divide the coefficient of the first term by the coefficient of the divisor: (-15x^5) / (-3x^2) = 5x^3.
Multiply the divisor by the quotient obtained in step 1: -3x^2 * 5x^3 = -15x^5.
Subtract the product obtained in step 2 from the dividend: 15x^5 - (-15x^5) = 30x^5.
Repeat steps 1 to 3 for the next term: (-3x^3) / (-3x^2) = x, -3x^2 * x = -3x^3, -3x^3 - (-3x^3) = 0.
Repeat steps 1 to 3 for the last term: (-9x^2) / (-3x^2) = 3, -3x^2 * 3 = -9x^2, -9x^2 - (-9x^2) = 0.
Therefore, the result of the division is:
5x^3 + 0x + 3
Simplifying the expression, we get:
5x^3 + 3
Therefore, the correct answer is (C) −5x^3 + x + 3.