Factor 9x^2+24x+16

Problem

9*x^2+24*x+16

Solution

1. Identify the structure of the quadratic expression a*x^2+b*x+c where a=9 b=24 and c=16

2. Recognize that the first term 9*x^2 is a perfect square, (3*x)^2 and the last term 16 is a perfect square, 4^2

3. Check if the middle term 24*x fits the pattern of a perfect square trinomial a^2+2*a*b+b^2 which factors into (a+b)^2

4. Verify the middle term by calculating 2*(3*x)*(4)

2*(3*x)*(4)=24*x

5. Apply the perfect square trinomial formula (a*x+b)^2

(3*x+4)^2

Final Answer

9*x^2+24*x+16=(3*x+4)^2

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