1 / 18

Factoring Quadratic Expressions

Factoring Quadratic Expressions. Specific Expressions. Trinomial – Binomial – Monomial – . Consisting of three terms (Ex: 5x 3 – 9x 2 + 3). Consisting of 2 terms (Ex: 2x 6 + 2x). Consisting of one term (Ex: x 2 ). Quadratic Expression.

dore
Download Presentation

Factoring Quadratic Expressions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Factoring Quadratic Expressions

  2. Specific Expressions • Trinomial – • Binomial – • Monomial – Consisting of three terms (Ex: 5x3 – 9x2 + 3) Consisting of 2 terms (Ex: 2x6 + 2x) Consisting of one term (Ex: x2)

  3. Quadratic Expression An expression in x that can be written in the standard form: ax2 + bx +c Where a, b, and c are any number except a ≠ 0.

  4. Factoring The process of rewriting a mathematical expression involving a sum to a product. It is the opposite of distributing. Example: PRODUCT SUM

  5. Factor If x2 + 8x + 15 = ( x + 3 )( x + 5 ) then x + 3 and x + 5 are called factors of x2 + 8x + 15 (Remember that 3 and 4 are factors of 12 since 3.4=12)

  6. Finding the Dimensions of a Generic Rectangle Mr. Wells’ Way to find the product for a generic rectangle: Make sure to Check Second, find missing WHOLE NUMBER dimensions on the individual boxes. First, find the POSITIVE Greatest Common Factor of two terms in the bottom row. 5 10x -15 2x 4x2 -6x 2x -3 Lastly, write the answer as a Product:

  7. The product of one diagonal always equals the product of the other diagonal. A Pattern with Generic Rectangles Example: 10x. -6x = -60x2 10x -15 4x2. -15 = -60x2 4x2 -6x

  8. Factoring with the Box and Diamond Factor: cis always in the top right corner Because of our pattern, the missing boxes need to multiply to: Fill in the results from the diamond and find the dimensions of the box: 3 +6 3x 4x (2x2)(6) 12x2 2x2 GCF 2x 4x 3x ___ Diamond Problem 7x x 2 ax2 is always in the bottom left corner Write the expression as a product: The missing boxes also have to add up to bx in the sum ( 2x + 3 )( x + 2 )

  9. Factoring Example Factor: Product c (3x2)(-10) -30x2 5 -10 15x -2x ax2c -2x 15x 3x2 GCF x ___ bx ax2 13x 3x -2 Sum ( x + 5 )( 3x – 2 )

  10. Factoring: Different Order Factor: Rewrite in Standard Form: ax2 + bx + c Product c (15x2)(-77) -1155x2 11 -77 33x -35x ax2c -35x 33x 15x2 GCF 5x ___ bx ax2 -2x 3x -7 Sum ( 5x + 11 )( 3x – 7 )

  11. Factoring: Perfect Square Factor: Product c (x2)(9) 9x2 3 9 3x 3x ax2c 3x 3x x2 GCF x ___ bx ax2 6x x 3 Sum ( x + 3 )( x + 3 ) ( x + 3 )2

  12. Factoring: Missing Terms Factor: Product c (9x2)(-4) -36x2 2 -4 6x -6x ax2c -6x 6x 9x2 GCF 3x ___ bx ax2 0 3x -2 Sum ( 3x + 2 )( 3x – 2 )

  13. Factoring: Which Expression is correct? Notice that every term is divisible by 2 Factor: If you use the box and diamond, the following products are possible: x2 ÷2 Which is the best possible answer?

  14. Factoring: Factoring Completely Factor: Ignore the GCF and factor the quadratic Reverse Box to factor out the GCF 5( x + 3 )( 2x – 1 ) Don’t forget the GCF Product c (2x2)(-3) -6x2 3 -3 6x -x ax2c -x 6x 2x2 GCF x ___ bx ax2 5x 2x -1 Sum

  15. Factoring: Factoring Completely Factor: Ignore the GCF and factor the quadratic Reverse Box to factor out the GCF 3x(x + 3)(x – 5) Don’t forget the GCF Product c (x2)(-15) -15x2 3 -15 3x -5x ax2c -5x 3x x2 GCF x ___ bx ax2 -2x x -5 Sum

  16. Factoring: Forgot to Factor a GCF Factor: No, it is not factored completely because one of the factors still has a GCF bigger than 1. When factoring the above expression a student came up with the following answer. Is it factored completely? Factor out the GCF with a reverse box Substitute the result: NOTE: I do not recommend relying on this. It can be used IF you forget to check for a GCF.

  17. Factoring: Just Factoring a GCF Factor: Reverse Box to factor out the GCF There is no longer a quadratic, it is not possible to factor anymore. There is not always more factoring after the GCF.

  18. Factoring: Ensuring “a” is Positive When the x2 term is negative, it is difficult to factor. Factor: Ignore the GCF and factor the quadratic Reverse Box to factor out the negative -( x + 6 )( x + 7 ) Don’t forget the GCF Product c (x2)(42) 42x2 6 42 6x 7x ax2c 6x 7x x2 GCF x ___ bx ax2 13x x 7 Sum

More Related