Factor 4x^2+13x+3

Problem

4*x2+13*x+3

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=4 b=13 and c=3

2. Calculate the product of a and c which is 4⋅3=12

3. Find two numbers that multiply to 12 and add up to the middle coefficient b=13 These numbers are 12 and 1

4. Rewrite the middle term 13*x using the two numbers found: 12*x+1*x

4*x2+12*x+x+3

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

(4*x2+12*x)+(x+3)

6. Factor out the greatest common factor from each group.

4*x*(x+3)+1*(x+3)

7. Factor out the common binomial (x+3)

(4*x+1)*(x+3)

Final Answer

4*x2+13*x+3=(4*x+1)*(x+3)

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