Questions: Factorization

Author

Millie Pike

Summary
A selection of questions for the study guide on factorization.

Before attempting these questions, it is highly recommended that you read Guide: Factorization.

Q1

Express each of the following expressions in their simplest factorized form.

1.1. \(\quad 7x+35\)

1.2. \(\quad 3x-51\)

1.3. \(\quad 6m+3n\)

1.4. \(\quad 5f+10+15k\)

1.5. \(\quad 10x-2+3y^2+3y\)

1.6. \(\quad 9xy-3x\)

1.7. \(\quad a^2+ab\)

1.8. \(\quad 4m^2-8nm+12m\)

1.9. \(\quad 12wx^2+16wx\)

1.10. \(\quad a^3b+ab^2+ ab^3\)

1.11. \(\quad x(x-6)+3(6-x)\)

1.12. \(\quad 3w+3z+xw+xz\)

1.13. \(\quad 2ab+ b^2-b-2a\)

1.14. \(\quad a^2 b+3a^2+ab+3a-2b-6\)

Q2

Express each of the following expressions in their simplest factorized form.

2.1. \(\quad x^2+6x+5\)

2.2. \(\quad x^2-3x-4\)

2.3. \(\quad x^2-4x+3\)

2.4. \(\quad 2x^2-13x+21\)

2.5. \(\quad 5x^2-10x+5\)

2.6. \(\quad x^2-xy-6y^2\)

2.7. \(\quad 12x^2 y^2+8xy^2-4y^2\)

2.8. \(\quad x^2-4yx-x+4y\)

2.9. \(\quad x^2+y^2-2xy\)

2.10. \(\quad x^2-y^2\)

2.11. \(\quad 9x^2 +3x -2\)

Q3

Using your workings from Q1 and Q2, solve the following expressions for \(x\) only.

3.1. \(\quad 7x+35 = 0\)

3.2. \(\quad x(x-6)+3(6-x)=0\)

3.3. \(\quad x^2-4x+3=0\)

3.4. \(\quad 12x^2 y^2+8xy^2-4y^2=0\)

3.5. \(\quad x^2-4yx-x+4y=0\)


After attempting the questions above, please click this link to find the answers.


Version history and licensing

v1.0: initial version created 04/25 by Millie Pike, as part of a University of St Andrews VIP project.

This work is licensed under CC BY-NC-SA 4.0.

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