Question

Divide 3x ^ 3 + 7x ^ 2 - 8x + 48 by x + 4

Answer 1

To divide the polynomial 3x^3 + 7x^2 - 8x + 48 by the binomial x + 4, use long division. The quotient will be 3x^2 - 5x - 20 with a remainder of -5x^2 - 8x + 48.

Step-by-step explanation:

To divide the polynomial 3x^3 + 7x^2 - 8x + 48 by the binomial x + 4, we use long division. Here are the steps:

1. First, divide the first term of the polynomial by the first term of the binomial. 3x^3 ÷ x = 3x^2.
2. Next, multiply the entire binomial by the result from the previous step. (x + 4) * 3x^2 = 3x^3 + 12x^2.
3. Subtract this result from the original polynomial to get the remainder. (3x^3 + 7x^2 - 8x + 48) - (3x^3 + 12x^2) = -5x^2 - 8x + 48.
4. Now, bring down the next term, -5x^2, and repeat the process.
5. Repeat steps 1-3 until you can no longer divide.

The quotient will be 3x^2 - 5x - 20, and the remainder will be -5x^2 - 8x + 48. So the final result of the division is (3x^2 - 5x - 20) with a remainder of -5x^2 - 8x + 48.