Factor 3x^2+7x+2

Problem

3*x2+7*x+2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=7 and c=2

2. Find two numbers that multiply to a⋅c=3⋅2=6 and add to b=7 These numbers are 6 and 1

3. Rewrite the middle term 7*x using the two numbers found in the previous step.

3*x2+6*x+x+2

4. Factor by grouping by splitting the expression into two pairs.

(3*x2+6*x)+(x+2)

5. Factor out the greatest common factor from each pair.

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

6. Factor out the common binomial factor (x+2)

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

Final Answer

3*x2+7*x+2=(3*x+1)*(x+2)

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