1. Factor
It’s a big deal!

2. Any amount of terms
#1 GCF Always look for and pull out the Greatest Common Factor if the polynomial has one.

3. 1. 6x² + 4x – 8 Ans: 2(3x²+2x -4) 2. 25x³ - 5x² - 10x
GCF
1. 6x² + 4x – 8
Ans: 2(3x²+2x -4)
2. 25x³ - 5x² - 10x
Ans: 5x(5x²- x- 2)

4. Just two terms
Difference of squares
a² - b² = (a + b)(a – b)

5. 1. x² -16 Ans: (x + 4)(x – 4) 2. 4x² - 25 Ans: (2x – 5)(2x + 5)
Difference of squares
1. x² -16
Ans: (x + 4)(x – 4)
2. 4x² - 25
Ans: (2x – 5)(2x + 5)

6. Just Two terms Sum or Difference of cubes
a³ + b³ = (a + b)(a² - ab + b²)
a³ - b³ = (a – b)(a² + ab + b²)

7. Cubes 1. x³-y³ Ans: (x-y)(x² + xy + y² 2. 8a³+ 1
Ans: (2a + 1)(4a² - 2a + 1)
3. m³ -27
Ans: (m – 3)(m² + 3m + 9)

8. Three Terms Trinomial lead coefficient of one
x² + ax + b = ( x + ___)(x + ___)
what times what = last term
what plus what = middle term

9. 1. x² + 8x + 12 Ans: (x + 6)(x + 2) 2. x² -7x + 12 Ans: (x- 4)(x – 3)
Trinomial Lead Coef. 1
1. x² + 8x + 12
Ans: (x + 6)(x + 2)
2. x² -7x + 12
Ans: (x- 4)(x – 3)

10. Trinomial lead coefficient not one ax² + bx + c Guess and check
3 Terms
Trinomial lead coefficient not one
ax² + bx + c
Guess and check

11. Trinomial Lead Coef. Not 1
1. 2x² + 7x + 3
Ans: (2x +1)(x + 3)
2. 3x² + 8x + 4
Ans: (3x + 2)(x + 2)

12. 4 or more terms
Grouping
Group pairs or groups, and pull out a common factor.
Write down what the groups have in common, times what’s left over from left to right.

13. 1. xa – 2x + 6a – 12 Ans: (x + 6)(a – 2) 2. xm – 2x -6m + 12
Grouping
1. xa – 2x + 6a – 12
Ans: (x + 6)(a – 2)
2. xm – 2x -6m + 12
Ans: (x – 6)(m - 2)

14. Homework
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