Math Problem Statement

Factor the trinomial.

x2 + 4x − 12

Solution

To factor the trinomial x2+4x12x^2 + 4x - 12, we need to find two numbers that multiply to 12-12 (the constant term) and add to 44 (the coefficient of the middle term).

Let's follow the steps:

  1. Identify the coefficients:

    • a=1a = 1 (coefficient of x2x^2)
    • b=4b = 4 (coefficient of xx)
    • c=12c = -12 (constant term)
  2. Find two numbers that multiply to a×c=12a \times c = -12 and add to b=4b = 4:

    • The numbers that work are 66 and 2-2 because:
      • 6×2=126 \times -2 = -12
      • 6+(2)=46 + (-2) = 4
  3. Rewrite the middle term using these two numbers: x2+6x2x12x^2 + 6x - 2x - 12

  4. Factor by grouping: x(x+6)2(x+6)x(x + 6) - 2(x + 6)

  5. Factor out the common binomial: (x2)(x+6)(x - 2)(x + 6)

So, the factored form of the trinomial x2+4x12x^2 + 4x - 12 is (x2)(x+6)\boxed{(x - 2)(x + 6)}.

Would you like more details, or do you have any questions?

Related Questions:

  1. How do you factor trinomials when the leading coefficient is not 1?
  2. What is the difference between factoring by grouping and using the quadratic formula?
  3. Can all quadratic trinomials be factored using integers?
  4. How do you factor perfect square trinomials?
  5. What are the applications of factoring trinomials in real-world problems?

Tip: When factoring, always check your work by expanding the factors to ensure they multiply back to the original expression.

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Math Problem Analysis

Mathematical Concepts

Algebra
Factoring
Quadratic Equations

Formulas

Factoring quadratic trinomials

Theorems

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Suitable Grade Level

Grades 7-9