Factor 2x^2-x-3

Problem

2*x2−x−3

Solution

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

2. Find two numbers that multiply to a*c=2⋅(−3)=−6 and add to b=−1 These numbers are −3 and 2

3. Rewrite the middle term −x using the two numbers found: −3*x+2*x

2*x2−3*x+2*x−3

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

x*(2*x−3)+1*(2*x−3)

5. Factor out the common binomial factor (2*x−3)

(2*x−3)*(x+1)

Final Answer

2*x2−x−3=(2*x−3)*(x+1)

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