Cancel the Common Factors (x-3x^2+2)÷(x-3)

Problem

(x2−3*x+2)/(x−3)

Solution

1. Identify the numerator as a quadratic expression in the form a*x2+b*x+c

2. Factor the numerator x2−3*x+2 by finding two numbers that multiply to 2 and add to −3

3. Determine that the factors are −1 and −2 so x2−3*x+2=(x−1)*(x−2)

4. Rewrite the original expression using the factored form of the numerator.

5. Check for common factors between the numerator (x−1)*(x−2) and the denominator (x−3)

6. Conclude that there are no common factors to cancel because x−3 does not appear in the numerator.

Final Answer

(x2−3*x+2)/(x−3)=((x−1)*(x−2))/(x−3)

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