Factor 2x^2-5x-3

Problem

2*x2−5*x−3

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=−5 and c=−3

2. Calculate the product of a and c which is 2⋅(−3)=−6

3. Find two numbers that multiply to −6 and add to the middle coefficient b=−5 These numbers are −6 and 1

4. Rewrite the middle term −5*x using the two numbers found: 2*x2−6*x+x−3

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 2*x*(x−3)+1*(x−3)

6. Factor out the common binomial (x−3) to obtain the final factored form.

Final Answer

2*x2−5*x−3=(2*x+1)*(x−3)

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