Simplify 4tan(x)^2+tan(x)-3

Problem

4*tan2(x)+tan(x)−3

Solution

1. Identify the expression as a quadratic in terms of tan(x) Let u=tan(x) to see the structure 4*u2+u−3

2. Find two numbers that multiply to 4⋅(−3)=−12 and add to 1 These numbers are 4 and −3

3. Rewrite the middle term using these numbers: 4*tan2(x)+4*tan(x)−3*tan(x)−3

4. Factor by grouping the first two terms and the last two terms: 4*tan(x)*(tan(x)+1)−3*(tan(x)+1)

5. Factor out the common binomial (tan(x)+1)

Final Answer

4*tan2(x)+tan(x)−3=(4*tan(x)−3)*(tan(x)+1)

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