Find the zeros of the polynomial 𝑝(𝑥)=2𝑥3−18𝑥.
Question
Find the zeros of the polynomial 𝑝(𝑥)=2𝑥3−18𝑥.
Solution
To find the zeros of the polynomial p(x) = 2x^3 - 18x, follow these steps:
Step 1: Set the polynomial equal to zero.
2x^3 - 18x = 0
Step 2: Factor out the common factor, which is 2x in this case.
2x(x^2 - 9) = 0
Step 3: Now, set each factor equal to zero and solve for x.
2x = 0 => x = 0
x^2 - 9 = 0
Step 4: The equation x^2 - 9 = 0 is a difference of squares, which can be factored as (x - 3)(x + 3) = 0.
Setting each factor equal to zero gives:
x - 3 = 0 => x = 3
x + 3 = 0 => x = -3
So, the zeros of the polynomial p(x) = 2x^3 - 18x are x = 0, x = 3, and x = -3.
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