Maths Library

Factoring polynomials: Grade 12 math

This topic covers rewriting expressions as products of factors by taking out common terms or factorising quadratics. The worksheet gives structured practise in identifying common factors and factorising trinomials.

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What this covers

Factoring polynomials is taught in Grade 12 (age 17 to 18) as a topic to introduce. It sits in the Algebra strand.

Worked example

Factorise fully: x^2 - 5x - 14

  1. Find two numbers that multiply to -14 and add to -5
  2. The factor pairs of -14 include (-7, 2), and -7 + 2 = -5
  3. Write as double brackets: (x - 7)(x + 2)

Answer: (x - 7)(x + 2)

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Common numerical factor only, e.g., 6x + 9 = 3(2x + 3)
  2. Common algebraic and numerical factor, e.g., 4x^2 - 6x = 2x(2x - 3)
  3. Simple quadratic trinomials x^2 + bx + c with positive terms
  4. Quadratic trinomials x^2 + bx + c involving negative terms
  5. Difference of two squares and quadratics with a > 1, e.g., 2x^2 + 7x + 3

Common mistakes

  • Partially factorising by taking out only a numerical factor when a variable is also common
  • Confusing signs when factorising quadratics with a negative constant term

Curriculum links

Indicative matches to Common Core State Standards. Check wording and codes against the official document.

  • Factor quadratic and higher-degree polynomial expressions to reveal roots, symmetries, and key features of functions.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Factoring polynomials

Grade 12 math

Qs
6
Marks
18
NameDateScore / 18
1.
Factorise x2 + 11x + 28.
[3]
2.
Factorise x2 + 11x + 30.
[3]
3.
Factorise x2 + 13x + 42.
[3]
4.
Factorise x2 + 8x + 16.
[3]
5.
Factorise x2 + 3x + 2.
[3]
6.
Factorise x2 + 7x + 6.
[3]

Answer key

  1. (x + 4)(x + 7)Find two numbers that multiply to 28 and add to 11; They are 4 and 7
  2. (x + 5)(x + 6)Find two numbers that multiply to 30 and add to 11; They are 5 and 6
  3. (x + 6)(x + 7)Find two numbers that multiply to 42 and add to 13; They are 6 and 7
  4. (x + 4)(x + 4)Find two numbers that multiply to 16 and add to 8; They are 4 and 4
  5. (x + 1)(x + 2)Find two numbers that multiply to 2 and add to 3; They are 1 and 2
  6. (x + 1)(x + 6)Find two numbers that multiply to 6 and add to 7; They are 1 and 6