Factor 2x^2+13x+15

Problem

2*x2+13*x+15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=13 and c=15

2. Find two numbers that multiply to a⋅c=30 and add to b=13

3. Determine that the two numbers are 10 and 3 because 10⋅3=30 and 10 + 3 = 13$.

4. Rewrite the middle term 13*x using these two numbers: 2*x2+10*x+3*x+15

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*x*(x+5)+3*(x+5)

6. Factor out the common binomial (x+5) to obtain the final factored form.

Final Answer

2*x2+13*x+15=(2*x+3)*(x+5)

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