Factor 9x^2-6x-8

Problem

9*x2−6*x−8

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=9 b=−6 and c=−8

2. Calculate the product of a and c which is 9×−8=−72

3. Find two numbers that multiply to −72 and add to the middle coefficient b=−6 These numbers are −12 and 6

4. Rewrite the middle term −6*x using the two numbers found: 9*x2−12*x+6*x−8

5. Factor by grouping the first two terms and the last two terms: (9*x2−12*x)+(6*x−8)

6. Extract the greatest common factor from each group: 3*x*(3*x−4)+2*(3*x−4)

7. Factor out the common binomial (3*x−4) to obtain the final factored form.

Final Answer

9*x2−6*x−8=(3*x+2)*(3*x−4)

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