Factor 6x^2+11x+3

Problem

6*x2+11*x+3

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=6 b=11 and c=3

2. Calculate the product of a and c which is 6⋅3=18

3. Find two numbers that multiply to 18 and add to the middle coefficient b=11 These numbers are 2 and 9

4. Rewrite the middle term 11*x using the two numbers found: 2*x+9*x

6*x2+2*x+9*x+3

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

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

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

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

Final Answer

6*x2+11*x+3=(3*x+1)*(2*x+3)

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