Quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1)

To find the quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1), we can follow the steps given below. These steps make the polynomial division process simple.

Step 1: Divide the first term of the dividend by the first term of the divisor. Here, divide x³ by x to get x².

Step 2: Multiply the entire divisor (x + 1) by the result from Step 1 (x²) and subtract the result from the original polynomial. You will get a new polynomial: (3x² + 5x + 3) - (x²)(x + 1) = 2x² + 5x + 3.

Step 3: Repeat the process with the new polynomial. Divide the first term of the new polynomial (2x²) by the first term of the divisor (x) to get 2x.

Step 4: Multiply the entire divisor by the result from Step 3 (2x) and subtract from the current polynomial: (2x² + 5x + 3) - (2x)(x + 1) = 3x + 3.

Step 5: Divide the first term of the remaining polynomial (3x) by the first term of the divisor (x) to get 3.

Step 6: Multiply the entire divisor by the result from Step 5 (3) and subtract from the current polynomial: (3x + 3) - (3)(x + 1) = 0. The quotient is x² + 2x + 3.

• Quotient: The result of dividing one polynomial by another.

• Dividend: The polynomial that is being divided.

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

• Polynomial Division: A method similar to long division for dividing polynomials.

• Remainder: The part of the dividend that is left after the division process, if any.