Factor 6x^2-17x+5

Problem

6*x2−17*x+5

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=6 b=−17 and c=5

2. Find two numbers that multiply to a*c=6⋅5=30 and add to b=−17 These numbers are −15 and −2

3. Rewrite the middle term −17*x using the two numbers found: −15*x−2*x

6*x2−15*x−2*x+5

4. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

3*x*(2*x−5)−1*(2*x−5)

5. Factor out the common binomial factor (2*x−5)

(3*x−1)*(2*x−5)

Final Answer

6*x2−17*x+5=(3*x−1)*(2*x−5)

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