Factor x^2-11x+28

Problem

x2−11*x+28

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−11 and c=28

2. Find two numbers that multiply to the constant term c=28 and add up to the linear coefficient b=−11

3. Determine the factors of 28 Since the sum is negative and the product is positive, both numbers must be negative. The pairs are (−1,−28) (−2,−14) and (−4,−7)

4. Select the pair (−4,−7) because −4+(−7)=−11

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

Final Answer

x2−11*x+28=(x−4)*(x−7)

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