Question

describing modeling with zero pairs
if you are using algebra tiles to factor a trinomial of the form ax² + bx + c, when would you need to bring in zero pairs? why?

Explanation:

Step1: Understand zero - pair concept

Zero pairs are $+ 1$ and $-1$ tiles (or other additive inverses). They add up to 0 and do not change the value of the polynomial.

Step2: Consider trinomial factoring

When the coefficient $b$ (linear - term coefficient) or $c$ (constant - term coefficient) cannot be represented using the available tiles for the $x^{2}$, $x$, and unit tiles in a straightforward way for factoring. For example, if you need to adjust the number of $x$ - tiles or unit tiles to form a rectangular arrangement (which represents factoring), zero pairs can be added.

Step3: Explain the reason

Adding zero pairs allows for re - arranging the tiles to form a rectangle, which represents the factored form of the trinomial. It is a way to manipulate the polynomial visually without changing its value.

Answer:

You would need to bring in zero pairs when the existing tiles for the trinomial $ax^{2}+bx + c$ cannot be arranged into a rectangle (to represent factoring) without adjusting the number of $x$ or unit tiles. The reason is that zero pairs do not change the value of the polynomial but can be used to re - arrange the tiles to find the factored form.