Factor 2x^2-5x+2

Problem

2*x2−5*x+2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−5 and c=2

2. Find two numbers that multiply to a*c=2⋅2=4 and add to b=−5

3. Determine the factors of 4 that satisfy the condition: −4 and −1 since (−4)*(−1)=4 and −4+(−1)=−5

4. Rewrite the middle term −5*x using the two numbers found: 2*x2−4*x−x+2

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−2)−1*(x−2)

6. Factor out the common binomial (x−2) to obtain the final factored form.

Final Answer

2*x2−5*x+2=(2*x−1)*(x−2)

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