Factor 2x^2-9x-18

Problem

2*x2−9*x−18

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−9 and c=−18

2. Calculate the product of a and c which is 2×−18=−36

3. Find two numbers that multiply to −36 and add to the middle coefficient b=−9 These numbers are −12 and 3

4. Rewrite the middle term −9*x using the two numbers found: 2*x2−12*x+3*x−18

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−6)+3*(x−6)

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

Final Answer

2*x2−9*x−18=(2*x+3)*(x−6)

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