Factor x^2-13x+42

Problem

x2−13*x+42

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−13 and c=42

2. Find two numbers that multiply to c (which is 42 and add up to b (which is −13.

3. Determine the pair of numbers by testing factors of 42 Since the product is positive and the sum is negative, both numbers must be negative.

4. Test the factors: −6 and −7 satisfy the conditions because (−6)×(−7)=42 and (−6)+(−7)=−13

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

Final Answer

x2−13*x+42=(x−6)*(x−7)

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