Question

Use long division to divide x³+x²-2x+14 by x+3. Choose the correct quotient.

Answer 1

To divide x³+x²-2x+14 by x+3 using long division, follow these steps.

Step-by-step explanation:

To divide x³+x²-2x+14 by x+3 using long division, we follow these steps:

1. Start by dividing the first term of the dividend, x³, by the divisor x+3. The result is x².
2. Multiply the divisor x+3 by the quotient x², which gives us x³ + 3x².
3. Subtract x³ + 3x² from the original dividend, x³+x²-2x+14. This gives us -4x²-2x+14.
4. Bring down the next term, which is -2x.
5. Divide -4x²-2x+14 by the divisor x+3. The result is -4x-14.
6. Multiply the divisor x+3 by the quotient -4x, which gives us -4x²-12x.
7. Subtract -4x²-12x from the previous step from the remaining part of the dividend, -4x²-2x+14. The result is 10x+14.

Since we have no more terms to bring down and the degree of the remaining part of the dividend, 10x+14, is less than the degree of the divisor, x+3, the division is complete.

Therefore, the quotient of x³+x²-2x+14 divided by x+3 is x²-4x-4.