Download presentation

Presentation is loading. Please wait.

Published byValerie Hall Modified over 6 years ago

1
5.4 Factoring Quadratic Expressions

2
WAYS TO SOLVE A QUADRATIC EQUATION ax² + bx + c = 0 There are many ways to solve a quadratic. The main ones are: –Graphing –Factoring –Bottom’s Up –Grouping –Quadratic formula –Completing the square

3
By Graphing By looking at the roots, we can get the solutions. Here, the solutions are -2 and 4. y = (x + 2)(x – 4)

4
Golden Rules of Factoring

5
Example: Factor out the greatest common factor 4x 2 + 20x -12

6
Practice: Factor each expression a)9x 2 + 3x – 18 b)7p 2 + 21 c)4w 2 + 2w Solutions: a.) 3(3x 2 + x – 6) b) 7(p 2 + 3) c) 2w(2w + 1)

7
Factor Diamonds x² + 8x + 7 =0 = (x + 1) (x + 7) = 0 7 8 17 So your answers are -1 and -7

8
Practice: Solve by a factor diamond X 2 + 15x + 36 (x+3)(x+12)

9
Bottom’s up (Borrowing Method) 12 13 112 2x² + 13x + 6 =0 x² + 13x + 12 =0 = (x + 12) (x + 1) =0 2 2 = (x + 6) (x + 1) =0 2 So your answers are -6 and -1/2 Multiply by 2 to get rid of the fraction = (x + 6) (2x + 1) =0

10
Practice: Solve using Bottom’s Up/Barrowing Method 2x 2 – 19x + 24 (x-8)(2x-3)

11
Factor by Grouping -30 -7 3-10 2x² – 7x – 15 =0 2x² – 10x + 3x – 15 =0 2x(x – 5) + 3(x – 5) =0 (2x + 3)(x – 5)=0 So your answers are -3/2 and 5 Note: you are on the right track because you have (x-5) in both parenthesis

12
Practice: Factor by Grouping 3x 2 + 7x - 20 (x+4)(3x-5)

13
SHORTCUTS a 2 + 2ab + b 2 (a+b) 2 Example: 9x 2 – 42x + 49 (3x – 7) 2 Example: 25x 2 + 90x + 81(5x + 9) 2 a 2 - 2ab + b 2 (a - b) 2 a 2 - b 2 (a+b)(a - b) Example: x 2 – 64 (x + 8)(x – 8)

14
Practice Problems: Solve using any method a)3x 2 – 16x – 12 b)4x 2 + 5x – 6 c)4x 2 – 49 d)2x 2 + 11X + 12 Solutions: a)(x-6)(3x+2) b)(x+2)(4x-3) c)(2x+7)(2x-7) d)(x+4)(2x+3)

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google