Factor 15x^2+7x-2

Problem

15*x2+7*x−2

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=15 b=7 and c=−2

2. Calculate the product a*c by multiplying 15 and −2 which results in −30

3. Find two numbers that multiply to −30 and add to the middle coefficient b=7 These numbers are 10 and −3

4. Rewrite the middle term 7*x using the two numbers found: 10*x−3*x

15*x2+10*x−3*x−2

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

5*x*(3*x+2)−1*(3*x+2)

6. Factor out the common binomial (3*x+2)

(5*x−1)*(3*x+2)

Final Answer

15*x2+7*x−2=(5*x−1)*(3*x+2)

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