Factor 6x^2+5x+1

Problem

6*x2+5*x+1

Solution

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

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

3. Rewrite the middle term 5*x using the two numbers found in the previous step.

6*x2+2*x+3*x+1

4. Group the terms into two pairs to factor by grouping.

(6*x2+2*x)+(3*x+1)

5. Factor out the greatest common factor from each pair.

2*x*(3*x+1)+1*(3*x+1)

6. Factor out the common binomial factor (3*x+1)

(2*x+1)*(3*x+1)

Final Answer

6*x2+5*x+1=(2*x+1)*(3*x+1)

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