Math Problem Statement
Solve or factor the quadratic expression: x^2 - 7x + 12.
Solution
The expression in the image is:
To solve or factor this quadratic expression, we look for two numbers that multiply to (the constant term) and add up to (the coefficient of ).
Step-by-Step Factoring:
- Identify the coefficients: The quadratic is of the form , where , , and .
- Find two numbers that multiply to and add to :
- The numbers that multiply to and add up to are and .
- Factor the quadratic expression:
So, the factorization of the quadratic expression is:
Would you like any further details or explanations?
Here are 5 related questions you might find useful:
- What is the quadratic formula, and how can it be used to solve quadratics?
- How do you complete the square for a quadratic expression?
- What are the solutions (roots) of the equation ?
- How can you graph the quadratic function ?
- What are the applications of quadratic equations in real-world problems?
Tip: Always check your factored form by expanding it back out to ensure it matches the original expression!
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Factoring
Formulas
Factoring: (x - p)(x - q) = 0 where p and q are the roots
Theorems
Quadratic Theorem
Suitable Grade Level
Grades 7-9