Algebra tiles and rectangle formation

Grade 10s were busy making rectangles today our of the algebra tiles that represent a given trinomial.

Here is x^2+5x+6

And here is the same expression, but arranged to make a rectangle.  The dimensions of the rectangle (length and width) are x+2 and x+3.

We noticed some expressions make squares rather than rectangles.  Here’s x^2+4x+4, which is has dimensions (x+2).  We can call that (x+2)^2

Not all trinomials can be made into a rectangle or square.

We looked at the x coefficient and the constant and the dimensions of the final rectangle, and we discovered a trend.

X^2+5x+6  the dimensions will involve two numbers which have a sum of 5 and also a product of 6.

We know from above that the dimensions are (x+2) and (x+3)….2+3=5 and (2)(3)=6

We will continue to work with these relationships over the course of this term.