Quotient of (x³ + 8) ÷ (x + 2)

To find the quotient of (x³ + 8) ÷ (x + 2), we can follow the steps given below. These steps make the polynomial division process simple.

Step 1: Set up the division as synthetic or long division. Here, we will use long division.

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 this result: (x + 2) × x² = x³ + 2x².

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

Step 5: Repeat the process for the remaining terms: -2x² ÷ x = -2x, and so on. Continue this process until you bring down all terms from the dividend. The final quotient will be x² - 2x + 4 with a remainder of 0.

• Quotient: The result we get after dividing two polynomials.

• Polynomial: An expression consisting of variables and coefficients, involving terms in the form of x raised to a power.

• Dividend: The polynomial that is being divided.

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

• Remainder: The part left over after division which cannot be divided by the divisor anymore.