Factor 6x^2+17x+5

Problem

6*x2+17*x+5

Solution

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

2. Calculate the product of a and c which is 6⋅5=30

3. Find two numbers that multiply to 30 and add up to the middle coefficient b=17 These numbers are 15 and 2

4. Rewrite the middle term 17*x using the two numbers found: 15*x+2*x

6*x2+15*x+2*x+5

5. 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)

6. 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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