Factoring trinomials can be carried out either by hand or by using a graphing calculator. The TI-84 is a graphing calculator used for many mathematical applications. Factoring a trinomial by calculator uses the Zero Product Property to carry out the calculation. The “zeros” of an equation, where Y = 0, is the place where the graphed line of the equation crosses the horizontal axis. Setting the values of the intercepts equal to “0” is how the factors of the trinomial is calculated.

## Finding the Zeros

Press the "Y=" button on the TI-84 graphing calculator. This will display a screen to input the trinomial equation. For example, type in the equation: (15X^2) + (14X) - 8.

Enter the trinomial into the calculator. Include the “X” variables by pressing the "X,T,O,n" button. Press "Enter" when done.

Change the window view to best see the graphed equation by pressing the "Window" button. For the example equation, set the following: Xmin = -4.7; Xmax = 4.7; Xscl = 1; Ymin = -12.4; Ymax = 12.4; Yscl = 1; Xres = 1.

Press "2ND" and then "Trace" to access the calculations menu. Choose the “Zero” option from the calculations menu screen.

Place the cursor to the left of the x-intercept, using the arrow keys, and press "Enter."

Place the cursor to the right of the x-intercept and press "Enter."

Press "Enter" again to display the zero of the function. The value given for the “X” will be the answer for that intercept. Repeat the calculating process to obtain the second zero for the equation.

Convert each x-intercept value to a fraction. Enter the value, press "Math," choose "Frac" and press "Enter" twice.

## Calculating the Factors

Write out the original equation with the highest degree term on the left.

Write each zero in terms of “X”. For example, the first zero for the example is -4/3, which would be written as “X = -4/3”.

Multiply the equation by the denominator of the value. The example is written as “3X = -4”.

Set the equation to be equal to “0”; this is the answer for one of the factors of the original equation. The example would be written as “3X + 4 = 0”.

Write each factor enclosed in parentheses and set to zero. The full answer for the equation is: (3x + 4)(5X - 2) = 0.

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#### Photo Credits

- miguel ugalde