Division of Polynomials or algebraic expressions | Basic of Algebra<br /><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^2<br /><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 + 7<br /><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 - 2x<br /><br />Step 7: Subtract this result from the current polynomial.<br /><br />Subtract from :<br /><br />(-x^2 - 2x + 7) - (-x^2 - 2x) = 7<br /><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 .<br /><br />Final Answer:<br /><br />\frac{3x^3 + 5x^2 - 2x + 7}{x + 2} = 3x^2 - x + \frac{7}{x + 2}<br /><br /><br />#divisionofpolynomial #divisionofalgebra #algebra
