Factor 4x^2-28x+49

Problem

4*x^2−28*x+49

Solution

1. Identify the structure of the quadratic expression a*x^2+b*x+c where a=4 b=−28 and c=49

2. Recognize that the first term 4*x^2 is a perfect square, (2*x)^2 and the last term 49 is a perfect square, 7^2

3. Check if the middle term matches the pattern for a perfect square trinomial a^2−2*a*b+b^2=(a−b)^2

4. Verify the middle term by calculating $2(2x)(7) = 28x$.

5. Apply the formula for a perfect square trinomial since the middle term is −28*x

Final Answer

4*x^2−28*x+49=(2*x−7)^2

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