Factor x^2+30x+225

Problem

x^2+30*x+225

Solution

1. Identify the structure of the quadratic expression a*x^2+b*x+c where a=1 b=30 and c=225

2. Recognize that the expression may be a perfect square trinomial of the form a^2+2*a*b+b^2=(a+b)^2

3. Verify the terms by checking if the first term is a square, x^2=(x)^2 and the last term is a square, 225=(15)^2

4. Check the middle term to see if it equals 2*a*b which is $2(x)(15) = 30x$.

5. Apply the formula for a perfect square trinomial to write the factored form as (x+15)^2

Final Answer

x^2+30*x+225=(x+15)^2

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