Question 22 on the MAT0020

Question 22 on the MAT0020/24C Beginning Algebra State Exam

Factoring a Polynomial: A Trinomial

22. Identify a factor of the following trinomial:

A. B. C. D.

Solution: Identify a factor of the following trinomial:

The first step to factor this problem is to identify which method can be used to factor. In this case the factoring method is factoring a trinomial because a trinomial is given.

Make sure another factoring method such as factor out the Greatest Common factor can be completed first. If it can that should be completed first.

There are two ways to factor this polynomial: Trial and Error and Change to grouping

First Method: Trial and Error

We know that when we factor, the factored form will be:

We will first list the possible factors:

We must get the leading term of

The possibilities are:

We know that it must multiply to the last term of + 4.

The possibilities with signs are:

**Signs are VERY important**

Since the middle term is negative, and it must add to the middle term, then it must be either: or

Then try different combinations and simply each one to try get :

Ex.

The solution is:

Since the question only requires one of the factors, the solution is:

Note: This solution can be checked by simplifying through FOIL.

Second Method: Change to grouping

Solution: Identify a factor of the following trinomial:

In this method we want the trinomial to become a polynomial with four terms so we can perform grouping. There is a specific way to change the trinomial into a polynomial with four terms.

Step 1: Find the middle factors

Multiply the leading coefficient by the last constant term.

, we want to find factors that multiply to get this number (including the sign)

The factors must also add to the middle term coefficient, in this case -25.

The factors that multiply to +24 and add to -25 are: -24 and -1

Step 2: Rewrite the polynomial

We found the two coefficients to replace the middle term to form a polynomial with 4 terms.

The trinomial will now become:

It does not matter which number goes first, but since we are going to group you want to place factors next to terms they have something in common with. For example, place the “-24t” next to the “” because they have a “6t” in common.