Factoring a Trinomial
In biology, Punnett squares are used to show possible ways that traits can be passed from parents to their offspring.
Each parent has two genes for each trait. The letters representing the parent’s genes are placed on the outside of the Punnett square. The letters inside the boxes show the possible gene combinations for their offspring.
The Punnett square shows the gene combinations for fur color in rabbits.
Since the trinomial comes from multiplying two first-degree binomials, let’s review what happens when we multiply binomials using the FOIL method. Remember that to do factoring we will have to think about this process in reverse (you could say we want to ‘de-FOIL’ the trinomial).
Factoring ax² + bx + c
A quadratic is more difficult to factor when the coefficient of the squared term is not 1, because that coefficient is mixed in with the other products from FOIL of the two binomials.
If you need to factor a trinomial such as, you have to think about what combinations could give the 2x2 as well as the other two terms. In this example the 2x2 must come from (x)(2x), and the constant term might come from either (-1)(3) or (1)(-3). The hard part is figuring out which combination will give the correct middle term. This gets messy because all those coefficients will be mixed in with the middle term when you FOIL the binomials
Practice: Factor trinomials of the form in the following exercises.