How to Factor w/ TI 83/84 Graphing Calculator

Ontario Online Academy
1 Dec 201704:30
EducationalLearning
32 Likes 10 Comments

TLDRThis instructional video script guides viewers on how to factor an equation using a TI-83 or TI-84 calculator. It demonstrates the process by example, starting with the equation xΒ³ + 2xΒ² - 5x - 6. The script explains the initial step of identifying possible integer factors and then proceeds to show how to use the calculator's 'Y=' function to test these factors. The method involves entering the equation, switching to the '2nd' mode, and using the 'ENTER' key to substitute values and determine if each is a factor. The video concludes by finding that x + 1, x - 2, and x + 3 are the factors of the given equation, providing a clear and concise tutorial on the factoring process.

Takeaways
  • πŸ“š The video script is a tutorial on how to use a TI-83 or TI-84 calculator to factor an equation.
  • πŸ” The example equation given is x^3 + 2x^2 - 5x - 6.
  • πŸ€” The process involves identifying possible factors based on the leading coefficient of the equation, which in this case are Β±1, 2, 3, and 6.
  • πŸ“ The script explains the steps to input the equation into the calculator using the 'y=' function.
  • πŸ”’ The tutorial demonstrates how to use the calculator's second function to test potential factors by substituting values.
  • πŸ’‘ It shows that F(1) is not a factor, but F(-1), F(2), and F(-3) result in zero, indicating these are factors.
  • πŸ“‰ The script mentions a shortcut to quickly return to the previous screen by pressing '2nd Enter'.
  • πŸ“Œ The factors found are x + 1, x - 2, and x + 3.
  • 🚫 The script clarifies that x - 3 is not a factor as it does not result in zero when substituted into the equation.
  • πŸ“ The final step is to express the original equation as a product of its factors.
  • πŸ‘ The script concludes by summarizing the key steps and encouraging viewers to practice using the calculator for factoring.
Q & A

  • What is the main topic of the video script?

    -The main topic of the video script is how to use a TI-83 or TI-84 calculator to factor an equation.

  • What is the example equation given in the script?

    -The example equation given is x^3 + 2x^2 - 5x - 6.

  • Why is the coefficient of x^3 considered in the possible factors?

    -The coefficient of x^3 is considered because if it's 1, it simplifies the possible factors to be the integers 1, 2, 3, and 6.

  • What does the script suggest to do after identifying possible factors?

    -The script suggests to try all possible factors by evaluating the function at each factor to see if it results in zero.

  • How does the script instruct to input the equation into the calculator?

    -The script instructs to input the equation by pressing 'Y=', then entering the equation x^3 + 2x^2 - 5x - 6.

  • What calculator mode is used to evaluate the function for a specific value?

    -The script uses the second mode to evaluate the function for a specific value.

  • What does the script mean by 'FAR's one over to the right'?

    -This likely refers to navigating through the calculator's menu by pressing the '2nd' button and then the 'ENTER' button to access the function evaluation feature.

  • What does the script suggest to do if the function evaluation results in zero?

    -If the function evaluation results in zero, it suggests that the tested value could be a factor of the equation.

  • What is the final factored form of the example equation according to the script?

    -The final factored form of the example equation is x + 1, x - 2, and x + 3.

  • What is the script's advice on how to navigate back to the previous function evaluation screen?

    -The script advises to use the '2nd' button and 'ENTER' to navigate back to the previous function evaluation screen.

Outlines
00:00
πŸ“š Factoring Equations Using a TI-83/84 Calculator

This paragraph provides a tutorial on how to use a TI-83 or TI-84 calculator to factor an equation. The equation given is xΒ³ + 2xΒ² - 5x - 6. The process begins by identifying possible factors based on the leading coefficient of xΒ³, which is 1, suggesting the factors could be Β±1, Β±2, Β±3, and Β±6. The video script demonstrates how to input the equation into the calculator using the 'y=' function and then proceed to test each potential factor by substituting values into the equation to check for a zero result, indicating a factor. The steps include using the calculator's second mode to navigate through the process and the 'F1' function to evaluate the equation at specific x-values. The tutorial successfully identifies x + 1, x - 2, and x + 3 as factors of the given equation.

Mindmap
Keywords
πŸ’‘TI-83/TI-84
The TI-83 and TI-84 are models of graphing calculators made by Texas Instruments. These calculators are commonly used in high school and college-level mathematics courses. In the video, the instructor demonstrates how to use these calculators to factor polynomial equations.
πŸ’‘Factor an equation
Factoring an equation involves breaking it down into simpler components, called factors, that when multiplied together give the original equation. The video focuses on factoring a cubic polynomial equation using the TI-83 or TI-84 calculator.
πŸ’‘Polynomial
A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication. The video uses a cubic polynomial, X^3 + 2X^2 - 5X - 6, as an example to demonstrate the factoring process.
πŸ’‘Y= function
The Y= function on the TI-83/TI-84 calculator is used to input equations that you want to graph or evaluate. In the video, the instructor inputs the polynomial equation into the Y= function to evaluate it at different values.
πŸ’‘Possible factors
Possible factors are the potential solutions or roots of an equation that can be tested to see if they satisfy the equation. In the video, the instructor lists the possible factors for the polynomial X^3 + 2X^2 - 5X - 6 as Β±1, 2, 3, and 6.
πŸ’‘Evaluate
To evaluate an equation means to calculate its value at specific points. The video shows how to use the calculator to evaluate the polynomial at different possible factors to identify the actual roots of the equation.
πŸ’‘Roots
Roots are the values of the variable that satisfy the equation, making it equal to zero. In the context of the video, finding the roots of the polynomial helps to determine its factors.
πŸ’‘Second Mode
Second Mode on the TI-83/TI-84 calculator is a function that allows users to access the secondary functions of buttons, such as clearing the screen. The video instructs viewers to use Second Mode to get a blank screen before performing further calculations.
πŸ’‘VARS function
The VARS (variables) function on the TI-83/TI-84 calculator allows users to access stored variables and functions. In the video, the instructor uses the VARS function to evaluate the polynomial at different possible factors.
πŸ’‘Factors
Factors are the simpler expressions that, when multiplied together, yield the original equation. In the video, after evaluating the polynomial at different possible factors, the instructor identifies X+1, X-2, and X+3 as the factors of the polynomial.
Highlights

Introduction to using the TI-83/84 calculator to factor an equation.

Explanation of the equation X^3 + 2x^2 - 5x - 6 to be factored.

Identification of possible factors based on the leading coefficient of X^3.

Demonstration of testing factors by substituting values into the equation.

Step-by-step guide on entering the equation into the calculator.

Using the calculator's 'second mode' to navigate through the equation setup.

Explanation of the 'fArce' function to test factors on the calculator.

Process of finding that X + 1 is a factor by substituting 1 into the equation.

Confirmation that X - 2 is a factor through the calculator's output.

Discovery that X + 3 is also a factor using the calculator.

Elimination of incorrect factors such as X - 4 and X - 3.

Final conclusion of the factors X + 1, X - 2, and X + 3 for the given equation.

Emphasis on the key steps of using the calculator for factoring equations.

Description of the 'y equals' function to input the equation into the calculator.

Guidance on using 'second enter' to quickly test different factors.

The importance of understanding the calculator's functions for educational purposes.

Conclusion and summary of the process for using the TI-83/84 to factor equations.

Transcripts

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