Math Problem Statement

Fully factorise x^2 + 12x

Solution

The expression provided is x2+12xx^2 + 12x. Let's fully factorize it.

Step-by-Step Factorization:

  1. Identify the greatest common factor (GCF) of the terms x2x^2 and 12x12x.

    • The GCF is xx, as both terms share this factor.
  2. Factor xx out: x2+12x=x(x+12)x^2 + 12x = x(x + 12)

Final Answer:

The fully factorized form is: x(x+12)x(x + 12)

Would you like further details or any clarifications?

Related Questions:

  1. How can the distributive property help verify this factorization?
  2. What happens when you set x(x+12)=0x(x + 12) = 0? What are the solutions?
  3. How can this factorization help in solving related quadratic equations?
  4. What is the significance of the GCF in factorization problems?
  5. How would this expression differ if a constant term were added?

Tip:

When factorizing, always look for the GCF first to simplify the process!

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Math Problem Analysis

Mathematical Concepts

Algebra
Factorization
Greatest Common Factor

Formulas

Factoring: GCF(a, b)
Distributive Property: a(b + c)

Theorems

Fundamental Theorem of Algebra

Suitable Grade Level

Grades 7-8