# Polynomial and Equation System Solver (PlySmlt2)

Many students (and even teachers) have no idea that a polynomial solver and system of equations solver is already installed in all TI-84 Plus series calculators. Because the interface can be slightly confusing to navigate, I still recommend creating a quadratic formula program to solve 2nd order polynomials, but for anything higher, the *PlySmlt2* app is the way to go.

### Getting to the App

To find the app, all you have to do is press the *apps* button and scroll down to *PlySmlt2. *Let’s start by learning how to work the polynomial root finder tool which solves all x-intercepts for a polynomial function.

### Polynomial Root Solver

The first screen you encounter contains all parameter options. To test the program, we are going to solve for a 3rd order polynomial (x^{3}). We will be solving for real numbers, and won’t be using any trigonometric functions so the radian/degree doesn’t matter. Therefore, we can leave the remaining five options as default. For our sample function let’s try to solve the polynomial x^{3} – 3x^{2} – 10x + 24 = 0. Make sure to choose the correct operator (+/-) before each value.

After that, just press *graph* to solve! It should provide you with the answers x = -3, 2, and 4. To confirm it is correct, I graphed the equation and provided the screenshot below. As you can see, the curve passes over the x-axis at the same three points! This tool is amazing for factoring polynomial functions you can’t figure out in your head.

### System of Equations Solver

This app also allows you to solve for a system of equations. Say you are given two equations: 5x + 2y = 1, and -3x + y = 0. Of course, this is simple enough that it wouldn’t take to long to solve manually, because there are only 2 equations with 2 unknown variables. However, you may one day encounter 5 equations with 5 unknown variables, and this tool will solve them for you in seconds. Anyways, back to my example, let’s test it! We can leave all the settings alone as long as 2 equations and 2 unknowns are selected. Next, input the system of equations and press *graph* to solve. If correct, you should find that the conditions x = 1/11 and y = 3/11 satisfies both equations!

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Great Article! Do you think that using matrices to solve systems is faster than using this app?