Factor 3x^2+11x+10

Problem

3*x2+11*x+10

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=3 b=11 and c=10

2. Find two numbers that multiply to a⋅c=30 and add to b=11

3. Determine that the two numbers are 5 and 6 since 5⋅6=30 and 5 + 6 = 11$.

4. Rewrite the middle term 11*x using these two numbers: 3*x2+6*x+5*x+10

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

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

Final Answer

3*x2+11*x+10=(3*x+5)*(x+2)

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