1. Questions over hw?

2. Skills Check 1. x2 + 2x – 15 2. x2 + 14x + 24 3. 2x2 + 6x – 36
Factor.
1. x2 + 2x – 15
2. x2 + 14x + 24
3. 2x2 + 6x – 36
4. 3x2 + 13x + 4
5. 4x2 + 16x + 15

3. EOCT Practice
Question of the Day

4. CCGPS Geometry Day 48 (10-18-13)
UNIT QUESTION: How are real life scenarios represented by quadratic functions?
Today’s Question:
What are special products when factoring quadratics?
Standard: MCC9-12.A.SSE.3a

5. Difference of Two Perfect Squares

6. Difference of Squares
A binomial with a subtraction sign in between terms that are both PERFECT SQUARES

7. To Factor Difference of Squares
One parenthesis is a plus and one is a minus.
Take the square root of each term.

8. Example

9. Example

10. Example

11. Example

12. Example

13. Perfect Square Trinomials
These are special too, but can be done using our usual method of factoring trinomials

14. Example

15. Example

16. 8. Factoring Special Cases: Word Problems
A square piece of cloth must be cut to make a tablecloth. The area needed is (16x2 – 24x + 9) in2. The dimensions of the cloth are of the form cx – d, where c and d are whole numbers. Find an expression for the perimeter of the cloth. Find the perimeter when x = 11 inches.
Examples! Be careful. #2 - #4 are tricky. You should know by now that you math teacher loves the tricky problems!
Normal… (x + 10)(x –10)
Hmm, x4 and 16 are both perfect squares… so (x2 + 4)(x2 – 4)… but wait a minute! One of those factors is a perfect square. I can factor it even more. (x2 + 4)(x –2)(x+2)… but beware! Don’t go “factor crazy” and try and factor the x It is one of those sums of squares that don’t factor.
Hmmm, again… 100 is a perfect square and so is 400, but I notice that the polynomials has a GCF of I can factor that out first. 100(x2 – 4). Now I can factor x So 100(x-2)(x+2)
Not a difference of squares, but maybe I can do what I did in #3 to factor this one. The GCF is 3. I can factor this to 3(x2 – 25) = 3(x-5)(x+5)
Not a polynomial, but It is a difference of squares. So (15x – 11y)(15x + 11y)

17. 9. Factoring Special Cases: Word Problems
A company produces square sheets of aluminum, each of which has an area of (9x2 + 6x + 1) m2. The side length of each sheet is in the form cx + d, where c and d are whole numbers. Find an expression in terms of x for the perimeter of a sheet. Find the perimeter when x = 3 m.
Examples! Be careful. #2 - #4 are tricky. You should know by now that you math teacher loves the tricky problems!
Normal… (x + 10)(x –10)
Hmm, x4 and 16 are both perfect squares… so (x2 + 4)(x2 – 4)… but wait a minute! One of those factors is a perfect square. I can factor it even more. (x2 + 4)(x –2)(x+2)… but beware! Don’t go “factor crazy” and try and factor the x It is one of those sums of squares that don’t factor.
Hmmm, again… 100 is a perfect square and so is 400, but I notice that the polynomials has a GCF of I can factor that out first. 100(x2 – 4). Now I can factor x So 100(x-2)(x+2)
Not a difference of squares, but maybe I can do what I did in #3 to factor this one. The GCF is 3. I can factor this to 3(x2 – 25) = 3(x-5)(x+5)
Not a polynomial, but It is a difference of squares. So (15x – 11y)(15x + 11y)

18. Classwork
SPW 13.9

19. Homework
Review Sheet