Factor x^2-13x+36

Problem

x2−13*x+36

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−13 and c=36

2. Find two numbers that multiply to the constant term c=36 and add to the linear coefficient b=−13

3. Determine the factors of 36 that satisfy the condition. Since the product is positive and the sum is negative, both numbers must be negative.

4. Test pairs of factors: (−1,−36) (−2,−18) (−3,−12) (−4,−9) and (−6,−6)

5. Select the pair (−4,−9) because −4+(−9)=−13

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

Final Answer

x2−13*x+36=(x−4)*(x−9)

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