Factor x^2-24x+144

Problem

x^2−24*x+144

Solution

1. Identify the structure of the quadratic expression x^2−24*x+144 which follows the form a*x^2+b*x+c

2. Recognize that the first term is a perfect square, x^2=(x)^2 and the last term is a perfect square, 144=12^2

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⋅x⋅12=24*x Since the middle term is −24*x the expression fits the pattern (x−12)^2

5. Write the factored form as the square of the binomial.

Final Answer

x^2−24*x+144=(x−12)^2

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