Factor x^2-12x-45

Problem

x2−12*x−45

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−12 and c=−45

2. Find two numbers that multiply to the constant term c=−45 and add to the linear coefficient b=−12

3. Test factors of −45 the pairs include (1,−45) (−1,45) (3,−15) and (−3,15)

4. Select the pair (3,−15) because 3 + (-15) = -12$.

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

Final Answer

x2−12*x−45=(x+3)*(x−15)

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