Factor x^2-14x+45

Problem

x2−14*x+45

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−14 and c=45

2. Find two numbers that multiply to the constant term c=45 and add up to the linear coefficient b=−14

3. Determine the factors of 45 that satisfy the condition. Since the product is positive and the sum is negative, both numbers must be negative. The numbers −5 and −9 work because (−5)×(−9)=45 and (−5)+(−9)=−14

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

Final Answer

x2−14*x+45=(x−5)*(x−9)

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