1. Warm Up Factor each of the following
64x4 – 49y2
125x
100x x + 81
x2 - 18x + 80

2. Polynomial Arithmetic/ Factoring Quiz
Simplify: (14x4 + 11x2 - 9x5) - (-14x + 5x5 - 12x2)
Simplify: (4 + 2n3) + (5n3 + 2n2 - 9)
Simplify: (6z2 - 5)(7z2 + 6z)
Factor: 16x4 – 100y6
Factor: 16x4 – 18x3 + 12x6
Factor: 512x9 + 27x12
Factor: 2x2 + 7x – 9
Factor: 169x x + 81

3. Polynomial Arithmetic/ Factoring Quiz
Simplify: (14x4 + 11x2 - 9x5) - (-14x + 5x5 - 12x2)
Simplify: (4 + 2n3) + (5n3 + 2n2 - 9)
Simplify: (6z2 - 6z - 5)(7z2 + 6z2 - 5)
Factor: 16x4 – 100y6
Factor: 16x4 – 18x3 + 12x6
Factor: 512x9 + 27x12
Factor: 2x2 + 7x – 9
Factor: 169x x + 81

4. Solving for x in quadratics
SWBAT solve for the value of x using factoring techniques and the zero product property
SWBAT solve for the value of x using the quadratic formula

5. Solving by Factoring
The standard form of quadratic equation is ax2 + bx + c = 0, where a ≠ 0.
Once a quadratic is in standard form we can solve for x by factoring and applying the zero product property

6. Zero Product Property Zero Product Property
If ab = 0, then a = 0 or b = 0
EXAMPLE: If (x + 3) (x – 7) = 0 then (x + 3) = 0 or (x – 7) = 0

7. Example
1. 16x2 = 8x

8. Example
2. x2 + 7x = 18

9. Example
3. 2x2 – 11x = -15

10. Practice Solve for x. 3x2 – 20x – 7 = 0 2x2 + 4x = 6 4x2 – 17x = 15

11. Warm Up Factor each of the following then solve for x
4x2 – 14x + 6 = 0
3x2 + 28x = -9
2x2 – 9x - 13= 5

12. Objective
SWBAT solve for the value of x using the quadratic formula

13. Warm Up Factor each of the following then solve for x
2x2 – 7x + 6 = 0
4x2 + 12x = -9
x2 – 8x + 20 = 5

14. Quadratic formula
sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution for X

15. Quadratic formula
The Quadratic Formula uses the a, b, and c from ax2 + bx + c, to solve for the value of X
The formula is:

16. Rules of the quadratic formula
you MUST have your equation arranged in the form ax2 + bx + c = 0
DO NOT drop the square root or the plus/minus
Remember order of operations under the square root
The 2a in the denominator of the Formula is underneath everything

17. Steps Step 1: Identify a, b, and c
Step 2: Plug in a, b, and c into the equation
Step 3: Simplify the equation
Step 4: SOLVE

18. Example
Find the values of x that make x2 + 3x – 4 = 0

19. Example
Find the values of x that make 2x2 – 4x = 3

20. Example
Solve x(x – 2) = 4

21. Example
Solve -4 + 9x2 + 12x = -4x2 + 6x

22. Practice 1) x2 – 5x + 3 = +3x 2) 4x2 + x – 6 = -2x2 3) 7x 2 + 3x = 2