Factor 9x^2-24x+16

Problem

9*x2−24*x+16

Solution

1. Identify the structure of the quadratic expression a*x2+b*x+c where a=9 b=−24 and c=16

2. Recognize that the first term 9*x2 is a perfect square, (3*x)2 and the last term 16 is a perfect square, 4

3. Check if the middle term matches the pattern for a perfect square trinomial a2−2*a*b+b2=(a−b)2

4. Verify the middle term by calculating 2(3x)(4) = 24x,w*h*i*c*h*m*a*t*c*h*e*s(t)*h*e*g*i*v*e*n*m*i*d(d(l))*e*t*e*r*m24x$ when the sign is considered.

5. Apply the formula for a perfect square trinomial (a−b)2 using a=3*x and b=4

Final Answer

9*x2−24*x+16=(3*x−4)2

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