Factor 3x^2+13x+4

Problem

3*x2+13*x+4

Solution

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

2. Find two numbers that multiply to a⋅c=3⋅4=12 and add to b=13

3. Determine the pair of numbers, which are 12 and 1 since 12⋅1=12 and 12 + 1 = 13$.

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

3*x2+12*x+x+4

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

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

6. Factor out the common binomial (x+4)

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

Final Answer

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

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