Quotient of (2x^4 – 3x^3 – 3x^2 + 7x – 3) ÷ (x^2 – 2x + 1)

To find the quotient of (2x⁴ – 3x³ – 3x² + 7x – 3) ÷ (x² – 2x + 1), we can follow the steps given below. These steps help simplify the polynomial long division process.

Step 1: Divide the first term of the dividend by the first term of the divisor. Here, divide 2x⁴ by x² to get 2x².

Step 2: Multiply the entire divisor by this quotient term (2x²) and subtract the result from the original polynomial.

Step 3: Repeat the process with the new polynomial obtained after subtraction until the degree of the new polynomial is less than the degree of the divisor.

Step 4: The result is the quotient, and any leftover polynomial is the remainder.

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

• Dividend: The polynomial that is being divided.

• Divisor: The polynomial by which we divide the dividend.

• Degree: The highest power of the variable in a polynomial.

• Remainder: The leftover polynomial after division when the degree of the result is less than that of the divisor.