Task: How can I factor this?
So far, you have mostly been working with expressions that are in the standard form ax² + bx + c. That is, the
terms are all positive. But, what
happens if a term is negative? Explore how to use algebra tiles to factor these
non-standard expressions by following the tutorials below.
3. [10 points] Factor x² - 3x + 2 with algebra tiles by:
a. Building and sketching a rectangular figure representing the expression.
b. Identifying the side lengths of the rectangle. Although it may sound counterintuitive, or
opposite of what you first think, label the lengths that are represented by
a negative
tiles as
1 or x.
-
c. Writing an equation showing that the area is equal to the product of is side length factors.
Check by multiplying the factors to get the original expression.
4. [10 points] Sometimes zero pairs must be added to close the rectangle. Adding zero pairs does not
change the value of the original expression since they, like their name implies, equate to 0. For
example, if you need to add an x tile, you MUST also add a - x tile to keep the balance of the
expression. Factor 2x² + x - 6 with algebra tiles by:
a. Building and sketching a rectangular figure representing the expression. Indicate the zero
pairs you added to close the rectangle.
b. Identifying the side lengths of the rectangle. Remember to use negative lengths appropriately.
c. Writing an equation showing that the area is equal to the product of its side length factors.
Check by multiplying the factors to get the original expression.