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Answer :
To divide the polynomial x^2+5x+6 by x+2 using long division, divide the leading terms, multiply the quotient by the divisor and subtract from the dividend, continue until the current dividend is zero, and the quotient is x+3.
To divide the polynomial x^2+5x+6 by x+2 using long division, follow these steps:
- Start by dividing the leading term of the polynomial, x^2, by the leading term of the divisor, x. The quotient is x.
- Multiply the divisor, x+2, by the quotient obtained in the previous step (x) and subtract the result from the original dividend. The result is 3x+6.
- Bring down the next term of the dividend, which is 5x.
- Repeat the process by dividing the new dividend, 3x+6, by the divisor, x+2. The quotient is 3.
- Multiply the divisor, x+2, by the quotient obtained in the previous step (3) and subtract the result from the current dividend (3x+6). The result is 0.
- Since the current dividend is now 0, the division is complete. The final quotient is x+3.
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