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 c (which is −30 and add to b (which is 7.

3. Determine the factors of −30 that satisfy the condition: 10 and −3

4. Verify the sum and product:

10⋅(−3)=−30

10+(−3)=7

5. 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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