Question

If you are using algebra tiles to factor a trinomial of the form (ax^2 + bx + c), then when do you need to bring in zero pairs?

a) When factoring a perfect square trinomial
b) When factoring a quadratic trinomial
c) When factoring a cubic trinomial
d) When factoring a difference of squares

Answer 1

In algebra tiles, zero pairs are used when factoring a quadratic trinomial to help visualize the factorization process, which is necessary when tiles can't be arranged into a rectangle without them.

Step-by-step explanation:

When using algebra tiles to factor a trinomial of the form ax² + bx + c, you need to bring in zero pairs for the option: b) When factoring a quadratic trinomial. Zero pairs are used in algebra tiles to represent the addition of a term and its negative equivalent, which nets to zero, aiding in the visualization of the factorization process. This is necessary when you cannot neatly arrange the tiles into a rectangle without them, which often occurs with non-perfect square trinomials. When factoring a difference of squares or a cubic trinomial, zero pairs are typically not required because the terms naturally cancel each other out or other techniques are needed respectively.