Algebraic Long Division

Maths: Edexcel A Level Pure Maths, topic 2.4.4

The Division Algorithm

The division of polynomials that contain more than one term is similar to the long division of whole numbers.

Set up the division

Set up the division

Step 1

Step 1

Divide $2x^3$ by $x$ to give $2x^2$ .
Write $2x^2$ on top of the division in line with the $x^2$ term of the polynomial.

Step 2

Step 2

Multiply $(x+2)$ by $2x^2$ to give $2x^3 + 4x^2$ .
Subtract $2x^3+4x^2$ from $2x^3-3x^2$ to give $-7x^2$ ..
The highest-order terms will always cancel out.
Write the resulting term of order $x^2$ underneath.

Step 3

Step 3

Divide $-7x^2$ by $x$ to give $-7x$ .
Write this above the division line.

Step 4

Step 4

Bring down the next term in the polynomial.

Step 5

Step 5

Multiply $x+2$ by $-7x$ and subtract this from $-7x^2+4x$ .

Step 6

Step 6

Divide $18x$ by $x$ to give $18$ .
Write this above the division line.

Step 7

Step 7

Bring down the final term of the polynomial.

Step 8

Step 8

Multiply $x+2$ by $18$ and subtract this from $18x+5$ .
-31 is the remainder of the division.

Step 8

Step 8

Answer

Answer

The quotient is the polynomial that is written above the division, and the remainder is the constant left over.

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