Factor 2x^2+3x-2

Problem

2*x2+3*x−2

Solution

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

2. Calculate the product of a and c which is 2⋅−2=−4

3. Find two numbers that multiply to −4 and add to the middle coefficient b=3 These numbers are 4 and −1

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

2*x2+4*x−x−2

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

2*x*(x+2)−1*(x+2)

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

(2*x−1)*(x+2)

Final Answer

2*x2+3*x−2=(2*x−1)*(x+2)

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