Factor 5x^2-9x-2

Problem

5*x2−9*x−2

Solution

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

2. Calculate the product a*c which is 5×−2=−10

3. Find two numbers that multiply to −10 and add to the middle coefficient b=−9 These numbers are −10 and 1

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

5. Factor by grouping the first two terms and the last two terms: 5*x*(x−2)+1*(x−2)

6. Factor out the common binomial (x−2) to obtain the final factored form.

Final Answer

5*x2−9*x−2=(5*x+1)*(x−2)

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