Quotient of x³ + 3x² + 5x + 3 by x + 1

To find the quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1), we can use polynomial long division.

Follow these steps to perform the division:

Step 1: Divide the leading term of the dividend x³ by the leading term of the divisor x to get x².

Step 2: Multiply x² by the entire divisor (x + 1) to get x³ + x².

Step 3: Subtract (x³ + x²) from the original polynomial, resulting in 2x² + 5x + 3.

Step 4: Repeat the process: Divide 2x² by x to get 2x, then multiply 2x by (x + 1) to get 2x² + 2x.

Step 5: Subtract 2x² + 2x from 2x² + 5x + 3, yielding 3x + 3.

Step 6: Divide 3x by x to get 3, then multiply 3 by (x + 1) to get 3x + 3.

Step 7: Subtract 3x + 3 from 3x + 3 to get 0, which means there is no remainder. Thus, the quotient is x² + 2x + 3.

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

• Dividend: The polynomial being divided.

• Divisor: The polynomial by which we divide.

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

• Remainder: The leftover part after the division is complete.