Is there a way to write a trinomial in factored form if you know the expanded form? (Distributive Property)

Question

I am currently in Algebra 1, and although it is annoying, we have to build rectangles made of algebra tiles and find the area as a product of its dimensions and as a sum of its parts. We are learning this as an intro to just using the distributive property to turn an expression like (x+1)(x+2) into x²⁺3x+2. It is fairly easy to do this, but I have come across a problem that asks me to do the opposite. That is, they want me to take 2x²+7x+6 and rewrite it as a product. I could do this with Algebra tiles, but I'm wondering if there is a shortcut like there is to get a sum from a product. Thanks, and I hope to get a response!

Answer 1

Using the algebra tiles are unnecessary.  You can use factoring by using different methods.

 

1) Factor out the GCF

2) Factor using FOIL

3) Factor by grouping

 

 

For example,

 

2x² + 7x + 6 = 2x² + 4x + 3x + 6

 

                    = 2x(x + 2) + 3(x + 2)

 

                    = (x + 2)(2x + 3)

 

 

What I did here was rewrite the expression to use factor by grouping.  I found two integers that multiply to the first and last terms, and add up to the middle terms  The two integers are 4 and 3.  Then, factored this to write an equivalent expression that is a sum of products.  The common factor came out to be (x + 2).  This method utilizes all methods mentioned above.