Question

(r^3+2r^2-7r-12) / (r+3) polynomial division

Answer 1

To divide the polynomial r^3+2r^2-7r-12 by r+3, we use polynomial long division. The quotient is r^2 - r - 4 and the remainder is 0.

Step-by-step explanation:

To divide the polynomial r^3+2r^2-7r-12 by r+3, we can use polynomial long division. Here are the steps:

1. Write the polynomial in descending order of powers of r: r^3+2r^2-7r-12
2. Divide the first term of the dividend by the first term of the divisor: r^3 / (r+3) = r^2
3. Multiply the divisor by the result of the previous step: (r+3) * r^2 = r^3 + 3r^2
4. Subtract the product from the dividend: (r^3+2r^2-7r-12) - (r^3 + 3r^2) = -r^2-7r-12
5. Repeat the process with the remainder: -r^2-7r-12 / (r+3)
6. Divide the first term of the new dividend by the first term of the divisor: -r^2 / (r+3) = -r
7. Multiply the divisor by the result of the previous step: (r+3) * -r = -r^2 - 3r
8. Subtract the product from the new dividend: (-r^2-7r-12) - (-r^2 - 3r) = -4r-12
9. The new dividend is -4r-12, which is a linear polynomial. Divide it by the divisor: -4r / (r+3) = -4
10. Multiply the divisor by the result of the previous step: (r+3) * -4 = -4r -12
11. Subtract the product from the new dividend: (-4r-12) - (-4r - 12) = 0

The quotient is r^2 - r - 4 and the remainder is 0. Therefore, the division is exact and the answer is the quotient: r^2 - r - 4.