Factor 3x^2+11x+6

Problem

3*x2+11*x+6

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=11 and c=6

2. Find two numbers that multiply to a⋅c=3⋅6=18 and add to b=11

3. Determine the pair of numbers, which are 9 and 2 since 9⋅2=18 and 9 + 2 = 11$.

4. Rewrite the middle term 11*x using the two numbers found: 3*x2+9*x+2*x+6

5. Factor by grouping the first two terms and the last two terms: 3*x*(x+3)+2*(x+3)

6. Factor out the common binomial factor (x+3)

Final Answer

3*x2+11*x+6=(3*x+2)*(x+3)

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