Division of Polynomials or algebraic expressions | Basic of Algebrabr br Steps for Long Division of Polynomials:br br Let's take a general polynomial division example:br br Divide by .br br Step-by-Step Solution:br br Step 1: Set up the division.br br Dividend: br br Divisor: br br br Start with the division symbol:br br \frac{3x^3 + 5x^2 - 2x + 7}{x + 2}br br Step 2: Divide the first term of the dividend by the first term of the divisor.br br Divide by , which gives .br br Now, write as the first term of the quotient.br br Step 3: Multiply the divisor by the first term of the quotient.br br Multiply by :br br 3x^2 \cdot (x + 2) = 3x^3 + 6x^2br br Step 4: Subtract this result from the dividend.br br Now subtract from :br br (3x^3 + 5x^2 - 2x + 7) - (3x^3 + 6x^2) = -x^2 - 2x + 7br br Step 5: Repeat the process with the new polynomial.br br Now, divide the first term of the new polynomial by , which gives .br br Write as the next term in the quotient.br br Step 6: Multiply the divisor by the new term of the quotient.br br Multiply by :br br -x \cdot (x + 2) = -x^2 - 2xbr br Step 7: Subtract this result from the current polynomial.br br Subtract from :br br (-x^2 - 2x + 7) - (-x^2 - 2x) = 7br br Step 8: Repeat the process one last time.br br Now divide the constant term by , but since is a constant and cannot be divided by , it becomes the remainder.br br Thus, the quotient is and the remainder is .