Factor 9x^2-42x+49

Problem

9*x^2−42*x+49

Solution

1. Identify the structure of the quadratic expression a*x^2+b*x+c where a=9 b=−42 and c=49

2. Recognize that the first term 9*x^2 is a perfect square, (3*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*(3*x)*(7)

2⋅3*x⋅7=42*x

5. Apply the perfect square trinomial formula (A−B)^2=A^2−2*A*B+B^2 where A=3*x and B=7

Final Answer

9*x^2−42*x+49=(3*x−7)^2

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