Factor 3x^2+7x+4

Problem

3*x2+7*x+4

Solution

1. Identify the coefficients a b and c from the quadratic expression a*x2+b*x+c where a=3 b=7 and c=4

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

3. Find two numbers that multiply to 12 and add up to the middle coefficient b=7 These numbers are 3 and 4

4. Rewrite the middle term 7*x using the two numbers found: 3*x+4*x

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

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

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

Final Answer

3*x2+7*x+4=(3*x+4)*(x+1)

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