2.4.4

Algebraic Long Division

Test yourself

The Division Algorithm

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

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Step 1

  • Divide 2x32x^3 by xx to give 2x22x^2.
  • Write 2x22x^2 on top of the division in line with the x2x^2 term of the polynomial.
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Step 2

  • Multiply (x+2)(x+2) by 2x22x^2 to give 2x3+4x2 2x^3 + 4x^2.
  • Subtract 2x3+4x22x^3+4x^2 from 2x33x22x^3-3x^2 to give 7x2-7x^2..
    • The highest-order terms will always cancel out.
  • Write the resulting term of order x2x^2 underneath.
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Step 3

  • Divide 7x2-7x^2 by xx to give 7x-7x.
  • Write this above the division line.
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Step 4

  • Bring down the next term in the polynomial.
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Step 5

  • Multiply x+2x+2 by 7x-7x and subtract this from 7x2+4x-7x^2+4x.
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Step 6

  • Divide 18x18x by xx to give 1818.
  • Write this above the division line.
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Step 7

  • Bring down the final term of the polynomial.
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Step 8

  • Multiply x+2x+2 by 1818 and subtract this from 18x+518x+5.
    • -31 is the remainder of the division.
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Answer

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

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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