Factor 5x^2-7x+2

Problem

5*x2−7*x+2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=5 b=−7 and c=2

2. Find two numbers that multiply to a⋅c=10 and add to b=−7

3. Determine the pair of numbers, which are −5 and −2 since (−5)*(−2)=10 and −5+(−2)=−7

4. Rewrite the middle term −7*x using these two numbers:

5*x2−5*x−2*x+2

5. Factor by grouping the first two terms and the last two terms:

5*x*(x−1)−2*(x−1)

6. Factor out the common binomial (x−1)

(5*x−2)*(x−1)

Final Answer

5*x2−7*x+2=(5*x−2)*(x−1)

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