Factor x^2-10x-24

Problem

x2−10*x−24

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−10 and c=−24

2. Find two numbers that multiply to the product a*c=−24 and add to the middle coefficient b=−10

3. Determine the factors of −24 that satisfy the condition. The numbers 2 and −12 work because 2⋅(−12)=−24 and 2 + (-12) = -10$.

4. Rewrite the expression using the binomial factors (x+p)*(x+q) where p and q are the numbers found in the previous step.

Final Answer

x2−10*x−24=(x−12)*(x+2)

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