how do you factor trinomials?

Question

im not sure how to factor a trinomial that doesnt have the same common factors. how do you do that ?

Answer 1

Some trinomials are not factorable. They are called prime trinomials. When you say that a trinomial doesn't have "the same common factors", are you referring to a common factor for each term?

For example,

2x²+6x-8  has a common factor between all three terms--2

But many trinomials that lack this kind of common factor can still be factored. They are factored by the FOIL method. Let's look at the same example. First we pull out the 2:

=2(x²+3x-4)

We can take the part in parentheses and make it look like this:

=2(x + ?)(x + ?)

The ? marks refer to numbers which can multiply together to make -4 and which add together to make 3 in this example

=2(x + 4)(x - 1)

4 and -1 multiply to give -4. And 4 and -1 add to give 3. So when we multiply out the terms using the FOIL method, we get x² + 3x - 4.

If our starting question was x² + 3x - 4, there is no common factor, but the entire trinomial is factorable.

Some trinomials cannot be factored and are called prime. For example:

x² + 3x + 4

There are ways to get the solutions for this trinomial. The easiest way is to use the quadratic formula, but completing the square can also work in many cases.

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