Factor x^2-3x-40

Problem

x2−3*x−40

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−3 and c=−40

2. Find two numbers that multiply to the product a*c=−40 and add to the coefficient b=−3

3. Determine the pair of numbers by testing factors of −40 The numbers 5 and −8 satisfy both conditions because 5×(−8)=−40 and 5 + (-8) = -3$.

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

Final Answer

x2−3*x−40=(x−8)*(x+5)

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