Post by

Alejandrina Reynoso

 Hello Everyone

This assignment was more complicated than I anticipated. It took me a long time to figure out how to to the factorization and to research the different methods. It was challenging to use the template, so I removed the box. I hope I got it right even though it is late, tried my best to finish sooner, but it was impossible. 

Factoring Trinomials Guide

Description of Method: 

The box method is used to help factor quadratic polynomials by making it easier to separate the greatest common factor of the coefficient and the last term (The Box Method for Factoring, 2016). The box consists of four-square boxes where you insert the leading term in the upper left-hand corner and the last term in the bottom right hand corner. The two empty boxes you will use to write the two factors of the sum of a and c. 

Example. 

Trinomial: 3×2 + 10x -8

a = 3×2 , b = 10x , c = -8

Example. 

Trinomial: 3×2+11+ 6x

a = 3×2 , b = 11x , c = 6

Step 1: Multiply a and c: 3×2 times -8 = -24                   Step 1: Multiply a and c: 3×2 times 6 = 18

Step 2: Find a product for a and c that will sum b           Step 2: Find a product for a and c that will sum b

Step 3: Factors of -24 that sum 10 are: (-2, 12)               Step 3: Factors of 18 that sum 11 are: (9,2)

Step 4: Draw a box of four squares and insert a in          Step 4: Draw a box of four squares and insert the numbers 

upper left-hand corner and c in bottom right-

corner                                                                     

Step 5: Now you will find the greatest common              Step 5: Find the greatest common factor 

factor of all numbers.                        3    -2                                                       3           2     

3×2 -2x

12x    -8

 3×2 2x

9x 6

                                     x                                      

3×2 and -2x is x                        x                                                                                                            

12x and -8 is 4                                                      

3×2 and 12x is 3                       4                

-2x and -8 is -2                                                                                                                             

 3

Step 6: Now we can write our factors.

(x + 4) (3x -2)

                                                                                           Step 6: Now we can write our factors

                                                                                                        (x + 3) (3x + 2)           

Check your work by expansion.                                                                    

We can use FOIL to check our answer.

  a   b    c     d                                                                     Check your work by expansion.

  (x+4) (3x-2)                                                                     We can use FOIL to check our answer.

Multiply: (ab, ad, bc and bd) then combine like                    a   b    c     d

terms.                                                                                     (x+3) (3x+2)

= 3×2 (-2x + 12x) -8                                                           Multiply: (ab, ad, bc and bd) then combine like terms.

= add like terms -2x + 12x                                               = 3×2 + (2x + 9x) +6

= 3×2 + 10x -8                                                                    = add like terms 2x + 9x                                                   

                                                                                           = 3×2 + 11x +6

The Box Method for Factoring. (2016, October 18). Retrieved from https://study.com/academy/lesson/the-box-method-for-factoring.html.

2.  

Post by Odalis Ordonez

12 days ago

Re: Week 6 | Discussion – Methods of Factoring Trinomials of the Form ax² + bx + c

Hello everyone,

I decided to research about the grouping factoring method. I liked this method because it is super simple and easy. When factoring trinomials by grouping, we first split the middle term into two terms. We then rewrite the pairs of terms and take out the common factor. 

The steps of factoring by grouping are:

• Step 1: Find the product ac.
• Step 2: Find  two factors of the product that add up to b
• Step 3: Write b as the sum of the two factors that you found. 
• Step 4: Group the two pairs of terms.
• Step 5: Take out the common factors from each group

Please see attached the template.

References

Khazanov, L., & Kirupaharan, N. (2010). What is the Best Way to Factor it? A Fresh Look at the Routine Problem of Factoring Quadratic Trinomials. MathAMATYC Educator, 2(1), 16.

 Factoring Trinomials Guide Description of Method: Factoring by grouping is the creation of two middle terms, which in many cases are like terms. The creation of these terms is the main focus of the process of factoring by grouping. Trinomial: x²+ 6x + 8 a = 1, b =6, c = 8 Step 1: Find the product ac (1)(8) = 8 Step 2: Find the two factors of 8 that add up 6 4 and 2 Step 3: Write 6x as the sum of 2x and 4x x²+2x+4x+8 Step 4: Group the two pairs of terms (x²+ 2x) + (4x+8) Step 5: Take out the common factors from each group. X(x+2) + 4(x+2) Step 6: Since the two quantities in parentheses are now identical. That means we can factor out a common factor of (x+2) (x+4) (x+2) Trinomial: 12 x²+ 34x+10 a = 12 , b = 34 , c = 10 Step 1: Find the product ac (12)(10) = 120 Step 2: Find the two factors of 120 that add up 34 4 and 30 Step 3: Write 34x as the sum of 4x and 30x 12x²+4x+30x+10 Step 4: Group the two pairs of terms (12x²+ 4x) + (30x+10) Step 5: Take out the common factors from each group. 2x(6x+2) + 5(6x+2) Step 6: Since the two quantities in parentheses are now identical. That means we can factor out a common factor of (x+2) (2x+5) (6x+2) Factoring Method: Factoring by Grouping Check your work by expansion. Check your work by expansion. (x+4) (x+2) (2x+5) (6x+2) = x²+ +2x+4x+8 = 12x²+ 4x+30x+10 = x²+ 6x+8 =12x²+34x+10