Factor X<Sup>2</Sup> + 2X + 2 Explained

Factor X^2 2 (problem with solution) from lunlun.com

Introduction:

Factor x² + 2x + 2 is a quadratic polynomial expression that is commonly found in algebraic problems. It is an expression that can be simplified by factoring, which involves finding two binomials that, when multiplied together, will result in the original expression. In this article, we will discuss in detail the process of factoring x² + 2x + 2.

Step-by-Step Solution:

Step 1: Check for the Constant Term:

The first step in factoring x² + 2x + 2 is to check if the constant term (the number without a variable) is a perfect square. In this case, the constant term is 2, which is not a perfect square.

Step 2: Find the Product of the Coefficient of the x² term and the Constant Term:

The next step is to find the product of the coefficient of the x² term (which is 1 in this case) and the constant term (which is 2). The product of 1 and 2 is 2.

Step 3: Find Two Numbers that Add up to the Coefficient of the x Term and Multiply to the Product Found in Step 2:

The third step is to find two numbers that add up to the coefficient of the x term (which is 2 in this case) and multiply to the product found in step 2 (which is 2). In this case, the two numbers are 1 and 2, since 1 + 2 = 3 and 1 x 2 = 2.

Step 4: Rewrite the Expression Using the Two Numbers Found in Step 3:

The fourth step is to rewrite the original expression using the two numbers found in step 3. This can be done by splitting the x term into two terms and replacing the constant term with the product found in step 2. The expression can be rewritten as x² + 1x + 2x + 2.

Step 5: Factor by Grouping:

The fifth and final step is to factor the expression by grouping the first two terms and the last two terms together. This can be done by factoring out the greatest common factor of each pair of terms. The expression can be factored as (x + 1)(x + 2).

Conclusion:

In conclusion, x² + 2x + 2 can be factored as (x + 1)(x + 2) by following the steps outlined above. Factoring is a useful tool in algebra that can simplify complex expressions and solve equations. By mastering the process of factoring, students can improve their algebraic skills and become more proficient in solving mathematical problems.