Gcmf of x2+2x

General
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gcmf of x2+2x

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GCMF of x^2 + 2x

Answer: To find the greatest common monomial factor (GCMF) of the expression x^2 + 2x, we need to determine the largest monomial that can be factored out of each term in the polynomial.

1. Understanding the Terms:

  • The polynomial x^2 + 2x consists of two terms: x^2 and 2x.
  • A monomial in this context would be any term of the form ax^b, where a is a constant and b is a non-negative integer.

2. Factoring Each Term:

Let’s break down each term:

  • The term x^2 can be rewritten as x \cdot x.
  • The term 2x is already in monomial form, which can be seen as 2 \cdot x.

3. Identifying the Common Factors:

Both terms share a common factor of x. Therefore, we can factor an x out of each term in the polynomial:

  • From x \cdot x, factoring out x leaves us with x.
  • From 2 \cdot x, factoring out x leaves us with 2.

Thus, the expression x^2 + 2x can be factored as x(x + 2).

4. Conclusion:

The greatest common monomial factor (GCMF) of the polynomial x^2 + 2x is x.

Therefore, the GCMF of x^2 + 2x is x. This means that x is the largest monomial that can divide both terms of the polynomial such that the resulting expression has integer coefficients.

[This explanation takes the student through the process of identifying and extracting the GCMF from a given polynomial, explaining each step clearly and breaking down the process to foster understanding.]