Factor x^2-13x+30

Problem

x2−13*x+30

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−13 and c=30

2. Find two numbers that multiply to c (30 and add to b (−13.

3. Determine the factors by testing pairs of numbers that multiply to 30 (−1,−30) (−2,−15) (−3,−10) and (−5,−6)

4. Select the pair (−3,−10) because −3+(−10)=−13

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

Final Answer

x2−13*x+30=(x−3)*(x−10)

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