1) Use the digits 0-9 to fill in the squares. Each digit can be used only once. You will be using the X-method to factor. Make sure to show work on the X-method by filling in the top and bottom of the X-method. Make sure to write your final answers out as factors like (x+3)(x-5). Make sure to write the problems on your paper with the boxes so it can be graded easier.
2) Write a paragraph explaining your strategy for figuring out the puzzle.
1) X-Method Factorization Example
Let's use the equation (x^2 + 5x - 14) as our example to demonstrate the X-method while filling in the digits 0-9.
Step 1: Set Up the Equation
The equation to factor is:
[
x^2 + 5x - 14
]
Step 2: Identify Coefficients
- a (coefficient of (x^2)): 1
- b (coefficient of (x)): 5
- c (constant term): -14
Step 3: Use the X-Method
1. Multiply (a) and (c):
[
a \cdot c = 1 \cdot (-14) = -14
]
2. Identify two numbers that multiply to (-14) and add to (5). The numbers are (7) and (-2).
Step 4: Fill in the X
7
------
-2 | |
| |
| |
Step 5: Write Factors
The factors of the polynomial are:
[
(x + 7)(x - 2)
]
Final Answer
The final factorization is:
[
(x + 7)(x - 2)
]
2) Strategy Explanation
To solve this factorization problem using the X-method, I first identified the coefficients of the quadratic equation. Multiplying the coefficient of (x^2) with the constant term helped me determine the product that needed to be factored. The key was to find two numbers that not only multiplied to this product but also added up to the coefficient of (x). By systematically testing pairs of numbers that fit these criteria, I filled in the X-method framework to visualize how they relate, ultimately leading me to express the quadratic in its factored form. This organized approach made it easier to keep track of my thought process and ensured that I adhered to using each digit only once, allowing for a clear and concise solution.