Question

Can anyone explain how to factor trinomials in steps please :)

Answer 1

Well, first what is a Trinomial?

A trinomial is a polynomial that contains three unlike terms, such as 2x^2 + 9x - 5. Factoring trinomials is just the opposite of multiplying. When a trinomial is factored, the answer appears in two sets of parentheses. If the terms in the parentheses are multiplied out, the answer is the beginning trinomial.

The Steps To Factoring a Trinomial

Begin with a trinomial. Using the example from above, factor the trinomial, 2x^2 + 9x - 5, by following these steps. The answer, after it is factored, will be in this form: (? ?)(? ?).

2
Calculate the first term for each set of parentheses. This is done by using the first term of the trinomial: 2x^2. Determine the way to multiply two terms to equal 2x^2. The only way this is done is by multiplying 2x times x. The 2x becomes the first unknown factor in the first parenthesis. The x becomes the first factor in the second set, looking like this: (2x ?)(x ?).

3
Calculate the second terms for the factoring. To do this, look at the 5, disregarding the signs, positive or negative, at this point. Determine a way to multiply 5 by two terms. The only way to do this is 5 times 1. These two numbers are placed in either order in the parentheses: (2x 5)(x 1) or (2x 1)(x 5).

4
Determine which set of parentheses is in the correct order. After the terms are calculated, the signs are placed within both sets of parentheses. To determine the signs, look at the last term in the trinomial: 9x. Looking at the outer and inner possibilities, we see that 2x times 1 plus 5 times x equals 7x. Therefore (2x 5)(x 1) cannot be the right order. Looking at (2x 1)(x 5) and multiplying the outers and inners, we calculate 2x times 5 and 1 times x. This gives the answer of 10x and 1x. By subtracting these two numbers, we find the 9x needed to complete this problem.

5
Fill in the signs. With (2x 1)(x 5) as the correct answers, the signs still need to be filled in. When multiplied, the answers found were 10x and 1x. In order to get the answer of 9x, the 10x must be positive and the 1x negative (10x - 1x = 9x). Therefore, the signs must be a positive 5 and a negative 1: (2x - 1)(x + 5).

6
Double-check the work by multiplying all factors out. This is done with the FOIL method. This method works by multiplying the firsts, the outers, the inners and then the lasts. By doing this, we get 2x times x, 2x times 5, -1 times x and -1 times 5. The answers are 2x^2 + 10x - 1x - 5. When this is simplified, the answer is the trinomial we started with: 2x^2 + 9x - 5.