Factor x^2-17x+72

Problem

x2−17*x+72

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−17 and c=72

2. Find two numbers that multiply to the constant term c=72 and add up to the linear coefficient b=−17

3. Determine the factors of 72 that satisfy these conditions. Since the product is positive and the sum is negative, both numbers must be negative.

4. Test pairs of factors: −8 and −9 satisfy the conditions because (−8)×(−9)=72 and (−8)+(−9)=−17

5. Write the expression in factored form (x+p)*(x+q) using the numbers found.

Final Answer

x2−17*x+72=(x−8)*(x−9)

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