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For example, we use 6x 2 + 5 x – 4 to find its factors as follows: Step 1: Graph the function y = 6 x 2 + 5 x – 4 with a calculator or an online graphing tool.

the original trinomial expression. Being aware of and skilled in more than one way to factor, the in structor can select the method or methods that best fit his or her students, likewise, the students are empowered to select a factoring method that best suits their understanding. Additionally, students make connections between factoring trinomials and their prior knowledge, which builds a stronger mathematical understanding of how factoring tech niques relate to other mathematical topics. These are a few ways to factor polynomials, specifically, trinomials. Burhanzade, H., & Aygör, N. (2015, June 18). Dif ficulties That Students Face During Factori zation Questions. Retrieved from https:// www.sciencedirect.com/science/article/pii/ S1877042815024003 Marks, H., Casey, C., Day, M., & Hayek, C. (2005). Algebra 1 (pp. 517). Virginia: McGraw Hill, Inc. Ratti, J.S., McWaters, M., & Skrzypek, L. (2019). Precalculus: A Right Triangle Approach (4th ed., pp. 47). Virginia: Pearson Educa tion, Inc. References

Step 2: Find x - intercepts of this function and write them out as equations: x = - 1.333 and x = + 0.50. Then, rearrange each equation so it is equal to zero, x + 1.33 = 0 and x – 0.5 = 0. The factors are first represented as decimals and then represented as fractions: x + 1 - 1/3 = 0 and x - 1/2 = 0. These two factors are set to zero because the roots of the trino mial, ( x + 1 - 1/3) ( x – 1/2) = 0. We remove the fractions by multiplying the factors by 3 and 2 respectively, or by the common factor, 6 on both sides of the equation to reach the integer format for the two factors (3 x + 4) (2 x – 1), which is our goal. The Factor by Polynomial Graphing method builds a connection between the zeros of a polynomial function, which are the x - intercept, and factors of the polynomial, or trinomial in this case. It helps students understand the relationship between find ing factoring and graphing the function. It shows students the intervals of the polynomial that are greater than, less than, or equal to zero. This meth od appeals to most students since they know how to graph. The disadvantages are access to the calcu lators or online graphing tools and some exams may not allow students to use graphing tools.

Check your solution:

To verify your solution for each method, you can use the distributive property. For example, (2 x – 1) (3 x + 4) = (6 x ) 2 + 8 x – 3 x – 4 = 6 x 2 + 5 x – 4, which is the original trinomial. Therefore we know we found the correct factors for the trinomial.

Zhenqiang Li Mathematics and Statistics, Old Dominion University & Tidewater Community College zlixx004@odu.edu

Conclusion

Fundamentally, factoring trinomials takes a trino mial and separates it into two binomials expres sions, which when multiplied together we reach

Virginia Mathematics Teacher vol. 46, no. 2

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