Factor 3x^2+14x+15

Problem

3*x2+14*x+15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=3 b=14 and c=15

2. Calculate the product a*c which is 3×15=45

3. Find two numbers that multiply to 45 and add to the middle coefficient b=14 These numbers are 9 and 5

4. Rewrite the middle term 14*x using the two numbers found: 9*x+5*x

3*x2+9*x+5*x+15

5. Factor by grouping the first two terms and the last two terms.

(3*x2+9*x)+(5*x+15)

6. Factor out the greatest common factor from each group.

3*x*(x+3)+5*(x+3)

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

(3*x+5)*(x+3)

Final Answer

3*x2+14*x+15=(3*x+5)*(x+3)

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