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 c (which is −40 and add to b (which is 3.

3. List the factor pairs of −40 to find the correct set: 8 and −5 satisfy both conditions because 8⋅(−5)=−40 and 8 + (-5) = 3$.

4. Rewrite 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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