Factor 5x^2-x-18

Problem

5*x2−x−18

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=5 b=−1 and c=−18

2. Calculate the product of a and c which is 5×−18=−90

3. Find two numbers that multiply to −90 and add to the middle coefficient b=−1 These numbers are −10 and 9

4. Rewrite the middle term −x using the two numbers found: 5*x2−10*x+9*x−18

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms: 5*x*(x−2)+9*(x−2)

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

Final Answer

5*x2−x−18=(5*x+9)*(x−2)

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