Factor x^2-12x+35

Problem

x2−12*x+35

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−12 and c=35

2. Find two numbers that multiply to equal c (35 and add to equal b (−12.

3. Determine the factors of 35 that satisfy the condition. Since the product is positive and the sum is negative, both numbers must be negative. The pairs are (−1,−35) and (−5,−7)

4. Select the pair (−5,−7) because −5+(−7)=−12

5. Write the factored form using these two numbers as (x+p)*(x+q)

Final Answer

x2−12*x+35=(x−5)*(x−7)

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