1. Review of Factoring
Unit R Lesson 2

2. Factoring
The process of finding polynomials whose product equals a given polynomial is called factoring.
Since 4𝑥+12=4 𝑥+3 , both 4 and
𝑥+3 are called factors of 4𝑥+12. Also,
4 𝑥+3 is called the factored form of 4x+12.

3. Irreducible Polynomial
A polynomial that cannot be written as a product of two polynomials with integer coefficients is a prime or irreducible polynomial.

4. Factor Out the Greatest Common Factor
6 𝑥 2 𝑦 3 +9𝑥 𝑦 𝑦 5

5. Factor Out the Greatest Common Factor
9 𝑦 5 + 𝑦 2

6. Factor Out the Greatest Common Factor
6 𝑥 2 𝑡+8𝑥𝑡+12𝑡

7. Factor Out the Greatest Common Factor
14 𝑚 4 𝑚+1 −28 𝑚 3 𝑚+1 −7 𝑚 2 𝑚+1

8. Factoring by Grouping
When a polynomial has more than three terms, it can sometimes be factored using factoring by grouping.

9. Factor by grouping.
𝑎𝑥+𝑎𝑦+6𝑥+6𝑦

10. Factor by grouping.
𝑚 𝑝 2 +7𝑚+3 𝑝 2 +21

11. Factor by grouping.
2 𝑦 2 +𝑎𝑧−2𝑧−𝑎 𝑦 2

12. Factor by grouping.
4 𝑥 3 +2 𝑥 2 −2𝑥−1

13. Factoring Trinomials
Factoring is the opposite of multiplication. Therefore, factoring requires using FOIL in reverse.

14. Factor the trinomial.
4 𝑦 2 −11𝑦+6

15. Factor the trinomial.
6 𝑝 2 −7𝑝−5

16. Factor the trinomial.
16 𝑦 𝑦 2 −16𝑦

17. Factoring Special Products
Perfect Square Trinomials 𝑥 2 +2𝑥𝑦+ 𝑦 2 = 𝑥+𝑦 2 𝑥 2 −2𝑥𝑦+ 𝑦 2 = 𝑥−𝑦 2

18. Factor the perfect square trinomial.
16 𝑝 2 −40𝑝𝑞+25 𝑞 2

19. Factor the perfect square trinomial.
169 𝑥 𝑥 𝑦 𝑦 4

20. Difference of Squares
𝑥 2 − 𝑦 2 = 𝑥+𝑦 𝑥−𝑦

21. Factor the polynomial.
4 𝑚 2 −9

22. Factor the polynomial.
256 𝑘 4 −625 𝑚 4

23. Factor the polynomial.
𝑎+2𝑏 2 −4 𝑐 2

24. Factor the polynomial.
𝑥 2 −6𝑥+9− 𝑦 4