1. Multiply (x+3)(2x-7) Factor 3. 42x – 7
Warm-Up
Multiply
(x+3)(2x-7)
Factor
3. 42x – 7

2. Homework Check

3. Factoring Trinomials and Difference of Two Perfect Squares

4. Sign Rule for Factoring Trinomials:
When the last term is POSITIVE…
The signs inside the parenthesis will be the SAME as the middle number’s sign

5. x2 +7x + 6
( )( ) x x
+ 6
+ 1

6. x2 + 9x + 14
( )( ) x x
+ 7
+ 2

7. x2 – 6x + 8
( )( ) x x
– 4
– 2

8. x2 – 10x + 16
( )( ) x x
– 8
– 2

9. Sometimes you can factor out a GCF 1st!

10. 2x2 – 16x + 24
2(x2 – 8x +12)
2( )( ) x x
– 6
– 2

11. You Try...
3y2 + 36y + 60
3(y +10)(y +2)
4x2 +24x + 32
4(x + 2)(x + 4)

12. Sign Rule for Factoring Trinomials:
When the last term is NEGATIVE…
The parenthesis will have DIFFERENT SIGNS.
The larger factor will have the SAME sign as the middle number

13. n2 + 2n – 48
( )( ) n n
+ 8
– 6

14. x2 + 8x – 20
( )( ) x x
– 2
+ 10

15. x2 – 4x – 21
( )( ) x x
+ 3
– 7

16. x2 – 9x – 36
( )( ) x x
+ 3
– 12

17. 2x3 + 18x2 + 28x

18. c4 + 2c3 – 80c2

19. 3x2 + 6x – 24

20. 5x2 + 5x – 10

21. 3x3 – 6x2 – 45x

22. 3x3 – 39x x

23. Difference of Two Perfect Squares

24. Factoring Difference of Two Squares
Both terms must be Perfect Squares and have a MINUS between them
Check the binomial for GCF
Use two sets of parenthesis (one’s a plus, one’s a minus)
Split up what it takes to make the 1st a perfect square and what it takes the 2nd to be a perfect square

25. Difference of Two Squares
Factor

26. Difference of Two Squares
Factor

27. 2x3 – 162x

28. 16x2 – 36

29. Factoring Trinomials when a is not equal to 1 Guess & Check Method

30. How to Factor a Trinomial
Check for GCF 1st. Divide out the GCF of each term if one exists.
When factoring ax2 + bx + c, first find factors of a and c.
Check the products of the inner and outer terms to see if the sum is b.
When c is POSITIVE, both signs inside the parentheses will be the same as the middle term.

31. 1. x2 + 9x + 14 +1 +2
+14 +7 1x
( )( )
x x

32. 2. 2x2 – 5x + 3 1x 2x -1 -3
( – )( – )
x x

33. 3. 5x2 + 11x + 2 1x 5x +1 +2
( )( )
x x

34. 4. 3x2 – 10x + 3 1x 3x -1 -3
( – )( – )
x x

35. 5. 2x2 – 7x + 5 1x 2x -1 -5
( – )( – )
x x

36. 6. 6x2 – 11x + 3 1x 2x 6x 3x -1 -3
( – )( – )
2x x

37. 7. 4x2 + 16x + 15 +1
+15 +3 +5 1x 2x 4x
( )( )
2x x

38. 8. 3x2 – 20x – 7 1x 3x 1 7
( )( )
x x –

39. 9. 2x2 + 3x – 5 1x 2x 1 5
( )( )
x x –

40. 10. 5m2 + 14m – 3 1m 5m 1 3
( )( )
m m –

41. 11. 2x2 – 11x – 21 1x 2x 1 3 7 21
( )( )
x x –

42. Sometimes you can factor out a GCF 1st!

43. 12. 14x2 – 32x + 18 2(7x2 – 16x + 9) 2( – )( – ) x 7x 1 9 1x 7x -1 -9-3
2( – )( – )
x x

44. Work
Factoring WS