2.4 Division Algorithm for Polynomials

Key Formulas

Solved Examples

Step 1

Divide $2x^2$ by $x$ . Result $2x$ . This is first term of quotient.

Step 2

Multiply $(x+2)$ by $2x$ : $2x^2 + 4x$ . Subtract this from dividend.

Step 3

$(2x^2 + 3x + 1) - (2x^2 + 4x) = -x + 1$ . New dividend is $-x + 1$ .

Step 4

Divide $-x$ by $x$ . Result $-1$ . Second term of quotient.

Step 5

Multiply $(x+2)$ by $-1$ : $-x - 2$ . Subtract.

Step 6

$(-x + 1) - (-x - 2) = 3$ . Remainder is 3.

Final Answer

Quotient: $2x-1$ , Remainder: 3

Interactive Solver