1. 6.6 Quadratic Equations
We will multiply binomials using the FOIL method.
We will factor trinomials
We will solve quadratic equations by factoring.
We will solve quadratic equations using the quadratic formula
We will solve problems modeled by quadratic equations.

2. Multiplying binomials using FOIL
We will multiply binomials using the FOIL method
Multiplying binomials using FOIL
Binomial - a simplified algebraic expression that contains two terms in which each exponent that appears on a variable is a whole number.
X+3 y-7 3x2 - 3x
FOIL - First, Outside, Inside, Last

3. Using FOIL (ax + b)(cx + d) = ax.cx+ ax.d + b.cx + b.d ax.cx = First
ax.d = Outside
b.cx = Inside
b.d = Last

4. Using Foil with numbers
(8-3)(4+8) We know = = 60
Using Foil:
8 . 4 = 32
8 . 8 = 64
= -12
= -24
= 60

5. Using FOIL for Binomials
(x + 8)(x-3) =
First x . x = x2
Outside x . -3 = -3x
Inside 8 . x = 8x
Last = -24
Put it together x2 + 5x - 24

6. Using FOIL for Binomials
(3x + 2)(4x-5) =
First 3x . 4x = 12x2
Outside 3x = -30x
Inside x = 8x
Last = -10
Put it together 12x2 -30x - 10

7. Factoring a trinomial where the coefficient of the squared term is 1
We will factor trinomials
Factoring a trinomial where the coefficient of the squared term is 1
Let take x2 + 10x +24.
We need to think of FOIL in Reverse
First we know the factors are:
(x+ )(x+ )
We know the plus signs because the coefficient of x is positive and because 24 is positive both signs are the same.
Now we need to think of factors of 24 that when added together equal , 4
( x + 6 )( x + 4 )

8. Factoring Trinomials with x2
If a trinomial can not be factored it is considered to be prime
x2 + 6x x x + 72

9. Factoring a Trinomial where a≠1
8x2 + 16x - 24
Find two terms whose product is 8x2
List all the factors of -24
Try all the combinations of these factors
Verify the factorization using the FOIL method

10. Working with 5x2 + 7x - 24
(x )(5x )

11. Factoring Trinomials with x2
x2 + x x x - 72

12. Factoring Trinomials with x2
x2 - 7x x x + 72

13. Solving a Quadratic Equation by Factoring
We will solve quadratic equations by factoring
Solving a Quadratic Equation by Factoring
A quadratic equation - Any equation that can be written in the form ax2 + bx + c = 0
Where a, b and c are real numbers a ≠ 0
Zero Product Principle
If AB = 0, then A = 0 or B = 0
Example: x2 + 5x + 6 = 0

14. Solving a factored quadratic equation
(x - 5)(x + 2) = 0
Either x - 5 = 0 or x + 2 = 0
X = {5, -2}
Check your results
Also this is x2 - 3x - 10 = 0
Check x = {5, -2} in the quadratic form.

15. Solving a quadratic equation by factoring
x2 + 7x = 18 x2 = 5x - 36

16. Solving a quadratic equation by factoring
x2 -16x = -3x x2 = -13x + 24

17. We will solve quadratic equations using the quadratic formula

18. Using the Quadratic Formula

19. Using the Quadratic Formula

20. Using the Quadratic Formula

21. Application of Quadratics