1Cademy - Finding the Quotient $$(3x^3 + 10x^2 + 6x

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Dividing Polynomials Using Synthetic Division

Example

Finding the Quotient $(3x^3 + 10x^2 + 6x - 2) \div (x + 2)$

Apply synthetic division to find the quotient and remainder when $3x^3 + 10x^2 + 6x - 2$ is divided by $x + 2$ . Write the coefficients of the dividend in the first row: $3$ , $10$ , $6$ , and $-2$ . The divisor is $x + 2$ , so place $c = -2$ in the divisor box. Bring down the first coefficient, $3$ , to the third row. Multiply $3$ by $-2$ to get $-6$ , and place it in the second row under the second coefficient $10$ . Add the column ( $10 + (-6)$ ) to get $4$ in the third row. Multiply $4$ by $-2$ to get $-8$ , placing it under $6$ . Add the column ( $6 + (-8)$ ) to get $-2$ . Multiply $-2$ by $-2$ to get $4$ , placing it under the final coefficient $-2$ . Add the column ( $-2 + 4$ ) to get $2$ . The third row numbers are $3$ , $4$ , $-2$ , and $2$ . The first three numbers give the quotient $3x^2 + 4x - 2$ , and the final number $2$ is the remainder.

Updated 2026-06-29

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OpenStax Intermediate Algebra

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