Factor x^2-7x-30

Problem

x2−7*x−30

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−7 and c=−30

2. Find two numbers that multiply to the constant term c=−30 and add to the linear coefficient b=−7

3. Determine the factors of −30 that satisfy the condition: the numbers are 3 and −10 since 3⋅(−10)=−30 and 3 + (-10) = -7$.

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

Final Answer

x2−7*x−30=(x−10)*(x+3)

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