Answers: Factorization
These are the answers to Questions: Factorization.
Please attempt the questions before reading these answers!
Q1
Note that you can rearrange the factorized brackets — the answer stays the same because the order of multiplication doesn’t matter.
1.1. \(7x+35 = 7(x+5)\).
1.2. \(3x-51 = 3(x-17)\).
1.3. \(6m+3n = 3(2m+n)\).
1.4. \(5f+10+15k = 5(f+2+3k)\).
1.5. \(10x-2+3y^2+3y = 2(5x-1)+y(3y+3)\).
1.6. \(9xy-3x = 3x(3y-1)\).
1.7. \(a^2+ab = a(a+b)\).
1.8. \(4m^2-8nm+12m = 4m(m-2n+3)\).
1.9. \(12wx^2+16wx = 4wx(3x+4)\).
1.10. \(a^3b+ab^2+ ab^3 = ab(a^2+b(1+b))\).
1.11. \(x(x-6)+3(6-x) = (x-6)(x-3)\).
1.12. \(3w+3z+xw+xz = (w+z)(3+x)\).
1.13. \(2ab+ b^2-b-2a = (2a+b)(b-1)\).
1.14. \(a^2 b+3a^2+ab+3a-2b-6 = (b+3)(a-1)(a+2)\).
Q2
Note that you can rearrange the factorized brackets — the answer stays the same because the order of multiplication doesn’t matter.
2.1. \(x^2+6x+5 = (x+5)(x+1)\).
2.2. \(x^2-3x-4 = (x-4)(x+1)\).
2.3. \(x^2-4x+3 = (x-3)(x-1)\).
2.4. \(2x^2-13x+21 = (2x-7)(x-3)\).
2.5. \(5x^2-10x+5 = 5(x-1)(x-1)\).
2.6. \(x^2-xy-6y^2 = (x-3y)(x+2y)\).
2.7. \(12x^2 y^2+8xy^2-4y^2 = 4y^2(3x-1)(x+1)\).
2.8. \(x^2-4yx-x+4y = (x-4y)(x-1)\).
2.9. \(x^2+y^2-2xy = (x-y)^2\) or \((y-x)^2\).
2.10. \(x^2-y^2 = (x-y)(x+y)\).
2.11. \(9x^2 +3x -2 = (3x-1)(3x+2)\).
Q3
3.1. You worked out in 1.1 that \(7x+35 = 7(x+5)\). Solving for \(x\) gives \(x =-5\).
3.2. You worked out in 1.11 that \(x(x-6)+3(6-x)=(x-6)(x-3)\). Solving for \(x\) gives \(x =3\) and \(x=6\).
3.3. You worked out in 2.3 that \(x^2-4x+3=(x-3)(x-1)\). Solving for \(x\) gives \(x =3\) and \(x=1\).
3.4. You worked out in 2.7 that \(12x^2 y^2+8xy^2-4y^2=4y^2(3x-1)(x+1)\). Solving for \(x\) gives \(x = 1/3\) and \(x=-1\).
3.5. You worked out in 2.8 that \(x^2-4yx-x+4y=(x-4y)(x-1)\). Solving for \(x\) gives \(x =4y\) and \(x=1\).
Version history and licensing
v1.0: initial version created 04/25 by Millie Pike, as part of a University of St Andrews VIP project.