Factor 2x^2-5x+3

Problem

2*x2−5*x+3

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−5 and c=3

2. Find two numbers that multiply to a⋅c=2⋅3=6 and add to b=−5

3. Determine the pair of numbers, which are −2 and −3 since (−2)*(−3)=6 and −2+(−3)=−5

4. Rewrite the middle term −5*x using the two numbers found: 2*x2−2*x−3*x+3

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−1)−3*(x−1)

6. Factor out the common binomial (x−1) to obtain the final factored form.

Final Answer

2*x2−5*x+3=(2*x−3)*(x−1)

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