Factor 2x^2-9x-5

Problem

2*x2−9*x−5

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=2 b=−9 and c=−5

2. Find two numbers that multiply to a⋅c=2⋅(−5)=−10 and add to b=−9

3. Determine the factors of −10 that satisfy the condition, which are −10 and 1

4. Rewrite the middle term −9*x using these two numbers: 2*x2−10*x+x−5

5. Factor by grouping the terms: (2*x2−10*x)+(x−5)

6. Factor out the greatest common factor from each group: 2*x*(x−5)+1*(x−5)

7. Extract the common binomial factor (x−5) to obtain the final factored form.

Final Answer

2*x2−9*x−5=(2*x+1)*(x−5)

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