Factor Trinomials with TI84 Calculator

Mathismagical
22 Apr 201504:16
EducationalLearning
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TLDRThe video explains how to factor trinomials using a calculator. It demonstrates the process with an example: factoring 6x² - 23x + 20. First, multiply 'a' and 'c' (6 and 20) to get 120, then find factors of 120 that add up to -23 using a calculator's table function. The factors -8 and -15, when divided by 6, yield the terms for the factors (3x - 4) and (2x - 5). Verification steps ensure the correct factors. Another example, 2x² + 19x + 24, is provided for practice, with the calculator revealing the factors as 2x + 3 and x + 8.

Takeaways
  • 🔢 Begin by multiplying a (6) and c (20) to get 120.
  • 🧮 Identify the factors of 120 that add up to -23.
  • 🖩 Use a calculator to find the factors of 120.
  • 📊 Go into the calculator's y equals function to factor 120 as 120 divided by x.
  • 🔍 Look at the table to find factors from the x and y1 columns.
  • ➕ Add the factors to see which pairs sum to -23 using y2.
  • ✔️ Identify the pair (-8, -15) that multiplies to 120 and adds to -23.
  • ➗ Divide each factor by a (6), simplifying to -4/3 and -5/2.
  • ✏️ Write the factors as (3x - 4) and (2x - 5) and verify them.
  • 🔄 Apply the same method to another trinomial: 2x^2 + 19x + 24, finding factors 3 and 16 that multiply to 48 and add to 19.
Q & A

  • What is the given trinomial to be factored in the script?

    -The given trinomial is 6x^2 - 23x + 20.

  • What are the initial steps in factoring the trinomial using the method described in the script?

    -The initial steps are to multiply 'a' and 'c', where 'a' is the coefficient of x^2 and 'c' is the constant term, which in this case are 6 and 20, respectively. This results in 120.

  • How does the script suggest finding the factors of 120 that also add up to -23?

    -The script suggests using a calculator to find the factors of 120 and then identify which pair of factors add up to -23.

  • What is the purpose of setting 'y1' to the factors of 120 in the calculator?

    -The purpose is to store the factors of 120 in 'y1' for further calculations and to find a pair that adds up to -23.

  • How is 'y2' used in the script to find the factors that add up to -23?

    -'y2' is set to equal x + y1, which is used to find the combination of factors that add up to -23 by looking at the values in the second table.

  • What factors of 120 were found in the script that add up to -23?

    -The factors found were -8 and -15, as they multiply to 120 and add up to -23.

  • How are the factors -8 and -15 divided by the coefficient 'a'?

    -The factors are divided by 6, resulting in -4/3 and -5/2, respectively.

  • What is the final factored form of the trinomial given in the script?

    -The final factored form is (3x - 4)(2x - 5).

  • How does the script suggest checking the factored form for correctness?

    -By multiplying the first terms, checking the last terms, and ensuring the middle term matches the original trinomial.

  • What is the additional practice problem provided in the script?

    -The additional practice problem is to factor the trinomial 2x^2 + 19x + 24 using the calculator.

  • What factors were found for the practice problem in the script?

    -The factors found for the practice problem were 3 and 16, which multiply to 48 and add to 19.

Outlines
00:00
🧮 Factoring Trinomials with Calculator Assistance

This paragraph explains how to factor the trinomial 6x² - 23x + 20 using a calculator. The process begins by multiplying the coefficients of x² (a = 6) and the constant term (c = 20) to get 120. The goal is to find factors of 120 that add up to -23. The paragraph details the use of a calculator to simplify this process by inputting 120/x into y1 and using the table function to find pairs of factors. By setting y2 to x + y1, the user can easily find the combination that sums to -23, which are -8 and -15. These factors are then divided by the leading coefficient (6) and simplified, resulting in the factors (3x - 4) and (2x - 5). The solution is verified by multiplying the factors to ensure they equal the original trinomial. A practice problem (2x² + 19x + 24) is provided, with instructions to clear previous entries in the calculator and follow similar steps, leading to the factors (2x + 3) and (x + 8).

Mindmap
Keywords
💡factoring trinomials
Factoring trinomials is a process in algebra where a quadratic expression is expressed as the product of two binomials. In the video, the process involves breaking down the trinomial 6x^2 - 23x + 20 into factors that can be easily handled and simplified, demonstrating how to approach and solve such problems systematically.
💡a times C
In the context of factoring trinomials, 'a times C' refers to multiplying the coefficient of the x^2 term (a) with the constant term (C). For the trinomial 6x^2 - 23x + 20, this multiplication (6 * 20 = 120) helps in finding factor pairs that sum to the middle coefficient (b, which is -23). This step is crucial in setting up the factorization process.
💡factors of 120
Finding the factors of 120 involves identifying all pairs of integers that multiply to 120. These factor pairs are used to determine which ones can sum to the middle coefficient (-23 in this case). This step is illustrated in the video using a calculator to systematically find and check these pairs.
💡y equals
The 'y equals' function on a calculator is used to input and manipulate equations. In the video, it is utilized to enter the expression 120 divided by x to find the factors of 120. This function allows the viewer to see a table of values, aiding in the process of identifying the correct factor pairs.
💡second table
The 'second table' refers to accessing the table of values generated by the calculator. This table displays the factors of 120 (from the y1 column) and their sums (from the y2 column). By examining this table, the user can find pairs of factors that meet the criteria needed to factor the trinomial correctly.
💡negative 23
Negative 23 is the middle coefficient of the trinomial 6x^2 - 23x + 20. The goal in factoring is to find two numbers that multiply to 120 (a*C) and add up to -23. This specific requirement guides the selection of factor pairs during the factorization process.
💡divide each factor by a
After identifying the factor pairs, each factor is divided by the leading coefficient 'a' (which is 6 in the example). This step simplifies the factors, making them ready for the next step in the factorization process. It converts the raw factor pairs into a form that can be written as binomials.
💡reduce
Reduction involves simplifying the fractions obtained after dividing the factors by 'a'. For instance, -8/6 simplifies to -4/3, and -15/6 simplifies to -5/2. This step ensures that the factors are in their simplest form, which is necessary for writing the final binomial factors.
💡3x - 4 times 2x - 5
These are the binomial factors of the original trinomial 6x^2 - 23x + 20. After simplifying the factor pairs, they are used to construct the binomials. The video checks the correctness of these binomials by multiplying them back to verify that they produce the original trinomial.
💡2x^2 + 19x + 24
This is another trinomial given as a practice example in the video. The process of factoring it using the calculator is demonstrated similarly to the previous example. The viewer is encouraged to apply the same steps to find the factors, thus reinforcing the method learned.
Highlights

Introduction to factoring trinomials with the assistance of a calculator.

The trinomial to be factored is 6x^2 - 23x + 20.

Step-by-step process begins with multiplying the leading coefficient (a) and the constant term (C).

Factors of 120 are sought to aid in the factoring process.

Utilization of a calculator to find factors of 120.

Explanation of using the calculator's 'Y1' to factor 120.

Setting up the calculator to find two numbers that add up to -23.

Using the calculator's 'Y2' to find pairs of numbers that sum to -23.

Identification of the factors -8 and -15 that meet the criteria.

Division of each factor by the leading coefficient (6) to simplify the expression.

Reduction of -8 by 6 to get -4/3 and -15 by 6 to get -5/2.

Formation of the factored expression 3x - 4 times 2x - 5.

Verification of the factored expression by checking the terms.

Encouragement to practice factoring with a new example: 2x^2 + 19x + 24.

Clearing of 'Y1' and 'Y2' on the calculator for practice purposes.

Finding factors 3 and 16 for the new trinomial example.

Final factored form of the example given as 2x + 3 times x + 8.

Transcripts

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