Find the Roots (Zeros) f(x)=2x^3-x^2-18x+9

Problem

ƒ(x)=2*x3−x2−18*x+9

Solution

1. Set the function to zero to find the roots of the polynomial.

2*x3−x2−18*x+9=0

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

(2*x3−x2)+(−18*x+9)=0

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

x2*(2*x−1)−9*(2*x−1)=0

4. Factor out the common binomial (2*x−1) from the expression.

(2*x−1)*(x2−9)=0

5. Factor the difference of squares x2−9 into (x−3)*(x+3)

(2*x−1)*(x−3)*(x+3)=0

6. Apply the Zero Product Property by setting each individual factor equal to zero and solving for x

2*x−1=0⇒x=1/2

x−3=0⇒x=3

x+3=0⇒x=−3

Final Answer

x=1/2,3,−3

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