Questions: 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.