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. Find two numbers that multiply to a⋅c=2⋅(−2)=−4 and add to b=−3

3. Determine the pair of numbers, which are −4 and 1 since (−4)⋅1=−4 and −4+1=−3

4. Rewrite the middle term −3*x using the two numbers found: 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 (x−2) to obtain the final factored form.

Final Answer

2*x2−3*x−2=(2*x+1)*(x−2)

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