Factor 3x^2+14x+8

Problem

3*x2+14*x+8

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=14 and c=8

2. Calculate the product of a and c which is 3×8=24

3. Find two numbers that multiply to 24 and add up to the middle coefficient b=14 These numbers are 12 and 2

4. Rewrite the middle term 14*x using the two numbers found: 12*x+2*x

3*x2+12*x+2*x+8

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)+2*(x+4)

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

(3*x+2)*(x+4)

Final Answer

3*x2+14*x+8=(3*x+2)*(x+4)

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