Factor 3x^2+5x+2

Problem

3*x2+5*x+2

Solution

1. Identify the coefficients a b and c from the quadratic expression a*x2+b*x+c where a=3 b=5 and c=2

2. Find two numbers that multiply to a⋅c=3⋅2=6 and add up to b=5

3. Determine that the two numbers are 2 and 3 because 2⋅3=6 and 2 + 3 = 5$.

4. Rewrite the middle term 5*x using these two numbers: 3*x2+3*x+2*x+2

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)+2*(x+1)

6. Factor out the common binomial (x+1) to obtain the final factored form.

Final Answer

3*x2+5*x+2=(3*x+2)*(x+1)

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