2x2 + 17x + 21 how to factor this with the box method

Question

I want to know how to factor the equation using the box method/unfoil method thank you

Answer 1

Hmmm.....  this isn't easy with the format here, but I'll give it a shot.

 

The coefficients of the terms in the trinomial are A, B, and C.

A=2  B=17  C=21

 

Draw a large X. Think of it as having 4 sections inside it. In the top section, multiply A x C, getting the answer 42. Write the answer to B in the bottom section (17). In the other two sections, you need to find two numbers whose product is 42 [AxC] and whose sum is 17 [B]. Those numbers are 3 and 14. Now you can make your box.

 

In the top left corner, write 2x^2 [which you get from the original problem].  In the top right corner, write 3x [which you get from the 3 and 14]. In the bottom left corner, write 14x [which you get from the 3 and 14]. In the bottom right corner, write 21 [which you get from the original problem]. 

 

On the outside of the box, you are going to factor on the right and bottom. I'll see if I can draw it here. The ... ... are just for spacing. If I wrote this out by hand, they would not be there.

 

_______________

|..2x^2..|..3x...|   x

|_______|______|

|...14x...|..21...|   +7

|_______|______|

  ...2x........+3

 

So the factors are (x+7) and (2x+3)

 

 

More info can be found here: http://www.dummies.com/education/math/algebra/factoring-trinomials-using-the-box-method/

 

Let me know if you have questions. Have a great day!