Quotient of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3)

To find the quotient of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3), we can follow the steps given below. These steps make the polynomial division process simple.

Step 1: Divide the first term of the dividend (x³) by the first term of the divisor (x²) to get the first term of the quotient, which is x.

Step 2: Multiply the entire divisor (x² + 4x + 3) by this term (x) and subtract the result from the original dividend (x³ + 6x² + 11x + 6).

Step 3: The new polynomial becomes 2x² + 7x + 6.

Step 4: Repeat the process: Divide 2x² by x² to get 2, multiply the divisor by 2, and subtract from the current polynomial.

Step 5: The remainder is x. So the quotient is x + 2 with a remainder of x.

Step 6: The complete division statement is: (x³ + 6x² + 11x + 6) = (x² + 4x + 3)(x + 2) + x.

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

• Dividend: The polynomial which is being divided.

• Divisor: The polynomial by which we divide.

• Remainder: The polynomial left over after division.

• Polynomial: An expression consisting of variables and coefficients.