Answer
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Step 1:I'll solve this polynomial factorization problem step by step:
Step 2:: Identify the polynomial
- We have the polynomial $$x^{2} + 2x
- This is a quadratic expression with two terms
Step 3:: Look for a common factor
- Notice that both terms share $$x$$ as a common factor
- We can factor out x
Step 4:: Rewrite the expression by factoring out x
x^{2} + 2x = x(x + 2)
Step 5:: Check if further factorization is possible
- $$x$$ is a factor
- (x + 2) cannot be factored further as it is a linear term - This is the fully factored form
Final Answer
Key Insights: - Always look for common factors first - In this case, x was common to both terms - The factored form clearly shows the structure of the original polynomial
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