1. Warm Up 1/9 Distribute: (2x – 3) (x + 4) x2y(9x – 10 + 11y)

2. STEPS FOR FACTORING
step 1: write it in standard form ax2 +bx + c
step 2: factor out GCF if possible
Step3: Check for a short-cut
step 4: Write what a, b, and c =
step 5: write 2 sets of ( )
put ax in each set
step 6: multiply a and c
step 7: what factors of step 6
add up to b?
step 8: simplify/reduce each set of ( ) if you can

3. Factoring: Follow the steps!
Ex. 1) 4x2 + 16x + 16
1) Is it in standard form?
4) a =1 b = 4 c = 4
4(x2 + 4x + 4)
2) Factor out the GCF if possible
3) Write 2 sets of ( ).
Put the ax term in the 1st and 3rd position.
4(x ___)(x ____)
5) Multiply a and c
1 x 4 = 4 write this number down above the b term.
6) What factors of step 3 add up to the b term? Insert the correct terms into position 2 and 4
1,4 or 2,2
4(x +2)(x+2)
7) Simplify each set of ( ) if you can.

4. Ex2: watch your signs Ex 2) 6x2 – 26x – 20 2(x-5)(3x+2)
2(3x2 – 13x -10) standard form/ GCF
2(3x ____)(3x ____) Two sets of ( ) ax term in each
3 *(-10) = Multiply a x c
-1, , , , , , , ,5
What factors add up to the b term? Place in 2nd and 4th position
2(3x -15)(3x + 2) Reduce
2(x-5)(3x+2)

5. Short-cut: difference of perfect squares
ALWAYS look for a GCF first
If you have (perfect square – perfect square)
Example: (x2 – y2)
Factor: (x +y) (x – y)
Ex. 3) 2a2 - 8
2(a2 – 4) GCF
2(a + 2)(a – 2) using short- cut easy

6. What if I have variables as a GCF?
Great news! I am brilliant and not afraid of variables!
Ex. 4) 12y3 – 27y
GCF out 1st
3y(4y2 - 9)
You should recognize short-cuts
3y(2y + 3)(2y – 3)

7. Lets add trig… rules are the same
Trig notation:
sin2q = sinq * sinq or sin2x = sinx * sinx
cos2q = cosq * cosq
tan2q = tanq * tanq
Our variables are usually x or q
Different from: sinq2 = sin(q * q) or sinx2 = sin(x*x)
cosq2 = cos(q *q )
tanq2 = tan(q *q )

8. Example: sin2(30) sin(30) * sin(30) ½ * ½ = ¼ Different from sin(30)21 2
sin(30) * sin(30)
½ * ½ = ¼
Different from sin(30)2
sin(30)(30) = sin (900)
=540 – 360 = 180 so sin180 = 0
sinx = opp/hyp

9. Ex5: sin2x + sinx

10. Short-cuts – show up often in trig
Ex 7: cos2x – 1
Is cos2x a perfect square is 1 a perfect square, are we subtracting? YES
Easy (cosx – 1)(cosx + 1) done 
Try this on your own : Ex 8: cot4x – 1
(cot2x – 1)(cot2x + 1)
check is this factored completely?
You can factor (cot2x – 1) again
(cotx – 1)(cotx + 1)(cot2x + 1) done 

11. Ex9: sin2x – 2sinx – 3 If this was x2 – 2x – 3 could you factor?
YES – GCF/ double bubble/ a*c / reduce…
(x __) (x __ )
1* -3 = -3 …what multiplies to -3 adds to 1?
Replace x with sinx
(sinx – 3)(sinx +1) -3 +1

12. Ex10: last one 6cos2x + cosx – 1
Think: 6x2 + x – 1
No GCF (6x )(6x )
6*-1 = -6 … what multiplies to -6 adds to 1?
Reduce and replace x with cosx
(2x + 1)(3x – 1)
(2cosx +1)(3cosx – 1) done  +3
- 2

13. Classwork – try on your own, when you finish check your answers with your group

14. Homework
Pre-calc factoring worksheet
Show all work