1. Solving Quadratic Equations ( x + 4) ( x + 6 ) ( x – 7) ( x – 3 ) ( x – 2) ( x + 8 ) Algebra Unit – Part 1 ( x + 1) ( x - 5 )

2. Why did you learn to factor a trinomial? You learned to factor a trinomial into TWO binomials in order to use those answers. In order to use those answers you have to set each binomial = to zero (0). ( X – 3 ) ( x + 5 ) = 0 If you multiply two binomials and the value of one of them is zero, then the whole product is zero.

3. Setting the binomial = to Zero The product ( x – 3 ) ( x + 5 ) = 0 If either binomial = zero then the whole things is zero. What number would make the 1st binomial = 0? 3 What number would make the 2nd binomial = 0? -5 That means if x = 3 or x = -5, the whole problem is 0. Therefore, our answer is x = 3 or x = -5.

4. Sample Problems In the middle of your sheet of notes fill in the answers as we go, by setting each binomial = to zero. ( x – 2 ) ( x + 8) = 0 X = 2 or x = -8 ( x – 7 ) ( x – 3 ) = 0 X = 7 or x = 3 ( x + 4 ) ( x + 6 ) = 0 X = -4 or x = -6 ( x + 1 ) ( x – 5 ) = 0 X = -1 or x = 5

5. Solving Basic Square Root Problems The easiest type of quadratics to solve is basic square root problems. They come in two forms: x2= 64 and x2 – 36 = 0 To solve the first one, all you do is take the square root of the number. X = √64 = 8 and -8 To solve the second one, you have to add 36 to both sides and then take the square root. x2 – 36 = 0 +36 +36 x2 = 36 X = √36 = 6 and-6

7. X = √81 = 9 and-9

8. x2= 9

9. X = √9= 3 and-3

10. x2 = 16

11. X = √16 = 4 and-4x2 – 25 = 0 +25 +25 x2 = 25 X = √25 = 5 and-5 x2 – 49 = 0 +49 +49 x2 = 49 X = √49 = 7 and-7 x2 – 4= 0 +4 +4 x2 = 4 X = √4= 2 and-2

12. Steps to solving regular quadratics Set the trinomial = to zero. Factor the trinomial into the product of binomials Set each binomial = to zero Solve for x Example Solve: x2+ 5x -24 = 0 Only way to get a negative at the end is multiply 1 positive & 1 negative, looking at middle number the bigger number needs to be positive. ( x + 8 ) ( x - 3) = 0 ( x + 8 ) = 0 or ( x – 3) = 0 X = -8 or x = 3

14. ( x - 9 ) ( x + 1) = 0

15. ( x - 9 ) = 0 or ( x + 1) = 0

18. x2 - 14x + 60 = 12

19. -12 -12

20. X2 -14x +48 = 0

21. ( x - 8) ( x - 6) = 0

22. ( x - 8 ) = 0 or ( x - 6) = 0

23. X = 8 or x = 6