What is the Quotient of (x^3 + 8) ÷ (x + 2)?

To find the quotient of (x^3 + 8) ÷ (x + 2), we can use polynomial long division. Follow these steps:

Step 1: Write the division in long division format. The dividend is x³ + 8, and the divisor is x + 2.

Step 2: Divide the first term of the dividend by the first term of the divisor. x³ ÷ x = x².

Step 3: Multiply the entire divisor by the result from Step 2. (x + 2) * x² = x³ + 2x^2.

Step 4: Subtract the result from Step 3 from the original dividend. (x³ + 8) - (x³ + 2x²) = -2x² + 8.

Step 5: Repeat the process with the new dividend -2x² + 8.

Step 6: Divide -2x² by x to get -2x.

Step 7: Multiply (x + 2) by -2x to get -2x² - 4x.

Step 8: Subtract -2x² - 4x from -2x² + 8 to get 4x + 8.

Step 9: Divide 4x by x to get 4.

Step 10: Multiply (x + 2) by 4 to get 4x + 8.

Step 11: Subtract 4x + 8 from 4x + 8 to get 0. The quotient is x² - 2x + 4 with a remainder of 0.

• Quotient: The result obtained after dividing one polynomial by another.

• Polynomial: An expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

• Long Division: A method used for dividing polynomials, similar to numerical long division.

• Dividend: The polynomial being divided.

• Divisor: The polynomial by which the dividend is divided.