Factor x^2-9x+18

Problem

x2−9*x+18

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−9 and c=18

2. Find two numbers that multiply to the constant term c=18 and add up to the linear coefficient b=−9

3. Determine the factors of 18 that satisfy these conditions. The pairs of factors for 18 are (1,18) (2,9) and (3,6) Since the sum must be negative and the product positive, both numbers must be negative.

4. Select the pair (−3,−6) because (−3)×(−6)=18 and (−3)+(−6)=−9

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

Final Answer

x2−9*x+18=(x−3)*(x−6)

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