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. Multiply the leading coefficient a and the constant term c to find the product a*c

9⋅−8=−72

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

4. Rewrite the middle term 6*x using the two numbers found in the previous step.

9*x2+12*x−6*x−8

5. Group the terms into two pairs to prepare for factoring by grouping.

(9*x2+12*x)+(−6*x−8)

6. Factor out the greatest common factor from each pair.

3*x*(3*x+4)−2*(3*x+4)

7. Factor out the common binomial factor (3*x+4) from the expression.

(3*x−2)*(3*x+4)

Final Answer

9*x2+6*x−8=(3*x−2)*(3*x+4)

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