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Practice Makes Perfect
Factor by Grouping
In the following exercises, factor by grouping.
1. \(ab+5a+3b+15\)
- Answer
-
\((b+5)(a+3)\)
2. \(8y^2+y+40y+5\)
- Answer
-
\((y+5)(8y+1)\)
3. \(9p^2−15p+12p−20\)
- Answer
-
\((3p−5)(3p+4)\)
4. \(mn−6m−4n+24\)
- Answer
-
\((n−6)(m−4)\)
5. \(2x^2−14x−5x+35\)
- Answer
-
\((x−7)(2x−5)\)
Factor Trinomials of the Form \(x^2+bx+c\)
In the following exercises, factor each trinomial of the form \(x^2+bx+c\).
6. \(p^2+11p+30\)
- Answer
-
\((p+5)(p+6)\)
7. \(n^2+19n+48\)
- Answer
-
\((n+3)(n+16)\)
8. \(x^2−8x+12\)
- Answer
-
\((x−2)(x−6)\)
9. \(y^2−18y+45\)
- Answer
-
\((y−3)(y−15)\)
10. \(5p−6+p^2\)
- Answer
-
\((p−1)(p+6)\)
11. \(8−6x+x^2\)
- Answer
-
\((x−4)(x−2)\)
12. \(x^2−12−11x\)
- Answer
-
\((x−12)(x+1)\)
13. \(x^2−2xy−80y^2\)
- Answer
-
\((x+8y)(x−10y)\)
14. \(m^2−64mn−65n^2\)
- Answer
-
\((m+n)(m−65n)\)
Factor Trinomials of the Form \(ax^2+bx+c\) Using Trial and Error
In the following exercises, factor completely using trial and error. Be sure to always check for a GCF first!
15. \(p^3−8p^2−20p\)
- Answer
-
\(p(p−10)(p+2)\)
16. \(3m^3−21m^2+30m\)
- Answer
-
\(3m(m−5)(m−2)\)
17. \(5x^4+10x^3−75x^2\)
- Answer
-
\(5x^2(x−3)(x+5)\)
18. \(2t^2+7t+5\)
- Answer
-
\((2t+5)(t+1)\)
19. \(11x^2+34x+3\)
- Answer
-
\((11x+1)(x+3)\)
20. \(4w^2−5w+1\)
- Answer
-
\((4w−1)(w−1)\)
21. \(6p^2−19pq+10q^2\)
- Answer
-
\((2p−5q)(3p−2q)\)
22. \(−16x^2−32x−16\)
- Answer
-
\(−16(x+1)(x+1)\)
Factor Trinomials of the Form \(ax^2+bx+c\) using the ‘ac’ Method
In the following exercises, factor using the ‘ac’ method. Be sure to always check for a GCF first!
23. \(5n^2+21n+4\)
- Answer
-
\((5n+1)(n+4)\)
24. \(4k^2−16k+15\)
- Answer
-
\((2k−3)(2k−5)\)
25. \(6y^2+y−15\)
- Answer
-
\((3y+5)(2y−3)\)
26. \(2n^2−27n−45\)
- Answer
-
\((2n+3)(n−15)\)
27. \(60y^2+290y−50\)
- Answer
-
\(10(6y−1)(y+5)\)
28. \(48z^3−102z^2−45z\)
- Answer
-
\(3z(8z+3)(2z−5)\)
29. \(16s^2+40s+24\)
- Answer
-
\(8(2s+3)(s+1)\)
30. \(48y^2+12y−36\)
- Answer
-
\(12(4y−3)(y+1)\)
31. \(x^4−x^2−12\)
- Answer
-
\((x^2+3)(x^2−4)\)
32. \(x^4−3x^2−28\)
- Answer
-
\((x^2−7)(x^2+4)\)
EXTRA:Mixed Practice
Factoring is a skill that many students find challenging at first, but it is also one that becomes increasingly valuable as you continue in mathematics. With practice, it gets more manageable and even starts to feel routine.
The following mixed review is provided to support your studying and help you build confidence with these essential skills.
In the following exercises, factor each expression using any method.
1. \(u^2−12u+36\)
- Answer
-
\((u−6)(u−6)\)
2. \(r^2−20rs+64s^2\)
- Answer
-
\((r−4s)(r−16s)\)
3. \(12y^2−29y+14\)
- Answer
-
\((4y−7)(3y−2)\)
4. \(6n^2+5n−4\)
- Answer
-
\((2n−1)(3n+4)\)
5. \(13z^2+39z−26\)
- Answer
-
\(13(z^2+3z−2)\)
6. \(3p^2+21p\)
- Answer
-
\(3p(p+7)\)
7. \(6r^2+30r+36\)
- Answer
-
\(6(r+2)(r+3)\)
8. \(24n^2+20n+4\)
- Answer
-
\(4(2n+1)(3n+1)\)
9. \(x^4−4x^2−12\)
- Answer
-
\((x^2+2)(x^2−6)\)
10. \((x+3)^2−9(x+3)−36\)
- Answer
-
\((x−9)(x+6)\)
This page titled 5.3.H: Homework was last modified on Mon, 06 Jul 2026 03:20:45 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Kiersten Purves.
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