Factor 9x^2+3x-2

Problem

9*x2+3*x−2

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=9 b=3 and c=−2

2. Multiply the leading coefficient a and the constant term c to find the product a*c=9⋅(−2)=−18

3. Find two numbers that multiply to −18 and add to the middle coefficient b=3 These numbers are 6 and −3

4. Rewrite the middle term 3*x using the two numbers found: 6*x−3*x

9*x2+6*x−3*x−2

5. Group the terms into two pairs to factor by grouping.

(9*x2+6*x)+(−3*x−2)

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

3*x*(3*x+2)−1*(3*x+2)

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

(3*x+2)*(3*x−1)

Final Answer

9*x2+3*x−2=(3*x+2)*(3*x−1)

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