Factor 2x^2+9x-5

Problem

2*x2+9*x−5

Solution

1. Identify the coefficients of the quadratic expression 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 pair of numbers, which are 10 and −1

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

5. Group the terms into two pairs: (2*x2+10*x)+(−x−5)

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

7. Factor out the common binomial (x+5) to obtain the final factored form.

Final Answer

2*x2+9*x−5=(2*x−1)*(x+5)

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