Math Problem Statement

Solve or factor the quadratic expression: x^2 - 7x + 12.

Solution

The expression in the image is:

x27x+12x^2 - 7x + 12

To solve or factor this quadratic expression, we look for two numbers that multiply to 1212 (the constant term) and add up to 7-7 (the coefficient of xx).

Step-by-Step Factoring:

  1. Identify the coefficients: The quadratic is of the form ax2+bx+cax^2 + bx + c, where a=1a = 1, b=7b = -7, and c=12c = 12.
  2. Find two numbers that multiply to cc and add to bb:
    • The numbers that multiply to 1212 and add up to 7-7 are 3-3 and 4-4.
  3. Factor the quadratic expression: x27x+12=(x3)(x4)x^2 - 7x + 12 = (x - 3)(x - 4)

So, the factorization of the quadratic expression is:

(x3)(x4)(x - 3)(x - 4)

Would you like any further details or explanations?

Here are 5 related questions you might find useful:

  1. What is the quadratic formula, and how can it be used to solve quadratics?
  2. How do you complete the square for a quadratic expression?
  3. What are the solutions (roots) of the equation x27x+12=0x^2 - 7x + 12 = 0?
  4. How can you graph the quadratic function x27x+12x^2 - 7x + 12?
  5. 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