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Find the zeros of the function $F(x)=x^3+8$

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Factor sums and differences of cubes

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Q. Find the zeros of the function

F(x)=x^3+8

Set Equation Equal: To find the zeros of the function $F(x) = x^3 + 8$ , we need to set the function equal to zero and solve for $x$ . $0 = x^3 + 8$
Rewrite Equation: We can rewrite the equation as $x^3 = -8$ to isolate the $x^3$ term on one side. $\newline$ $x^3 = -8$
Take Cube Root: To solve for $x$ , we take the cube root of both sides of the equation. $x = (-8)^{\frac{1}{3}}$
Find Zero: The cube root of $-8$ is $-2$ , so one of the zeros of the function is $x = -2$ . $\newline$ $x = -2$
Check for Complex Zeros: Since the function is a cubic polynomial and we have found only one real zero, we need to check if there are any complex zeros. However, since the polynomial is not given in a factorable form with real coefficients and the question does not ask for complex zeros, we conclude that the only real zero of the function is $x = -2$ .

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