November 23rd 2016 archive

Modeling Polynomials

Below, I solved various equations using algebra tiles.

 

(X+1)^2

= (X+1)(X+1)

= X(X-1)+1(X+1)

= x^2+X+X+1

= x^2 +2x+1

image

 

 

 

 

 

 

(X-1)^2

= (X-1)(X-1)

= X(X-1) + 1(X-1)

= X^2-X+X+1

= X^2-2X+1

image

 

 

 

 

 

 

(X+1) (X-1)

= X(X-1)+1(X-1)

= X^2-X+X-1

= X^2-1

image

 

 

 

 

 

(X-1)^3

= (X-1) (X-1) (X-1)

= x^2-X-X+1

= (x^2-2x+1)(X-1)

= x^3-3x^2+3x-1

This assignment taught me how to you the $latex coding directly in my blog post. Before, I couldn’t figure out how to show my polynomials online, but this really helped and I will definitely use this is the future. I also visually saw how polynomial are distributed, as well as what can be modeled and what cannot. For example, the last question ((X-1)^3) cannot be modeled because we do not have tiles to demonstrate cubes. The other 3 previous question were able to be modeled because they all used squares (rather than cubes).