Simplify 8cos(x)^2+cos(x)-9

Problem

8*cos2(x)+cos(x)−9

Solution

1. Identify the expression as a quadratic in terms of cos(x) Let u=cos(x) to see the structure 8*u2+u−9

2. Find two numbers that multiply to 8⋅(−9)=−72 and add to 1 These numbers are 9 and −8

3. Rewrite the middle term using these numbers: 8*cos2(x)−8*cos(x)+9*cos(x)−9

4. Factor by grouping the terms: 8*cos(x)*(cos(x)−1)+9*(cos(x)−1)

5. Factor out the common binomial (cos(x)−1) to obtain the final factored form.

Final Answer

8*cos2(x)+cos(x)−9=(cos(x)−1)*(8*cos(x)+9)

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