Factor x^2-9x+20

Problem

x2−9*x+20

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−9 and c=20

2. Find two integers that multiply to the constant term c=20 and add up to the linear coefficient b=−9

3. Determine the factors of 20 that satisfy the condition. The pairs are (1,20) (2,10) (4,5) (−1,−20) (−2,−10) and (−4,−5)

4. Select the pair (−4,−5) because −4+(−5)=−9 and (−4)×(−5)=20

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

Final Answer

x2−9*x+20=(x−4)*(x−5)

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