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Find the
y-coordinate of the
y-intercept of the polynomial function defined below.

f(x)=-x(x-3)(x^(2)+2)^(3)
Answer:

Find the $y$ -coordinate of the $y$ -intercept of the polynomial function defined below. $\newline$ $f(x)=-x(x-3)\left(x^{2}+2\right)^{3}$ $\newline$ Answer:

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Find the roots of factored polynomials

Full solution

Q. Find the

y

-coordinate of the

y

-intercept of the polynomial function defined below.

\newline

f(x)=-x(x-3)\left(x^{2}+2\right)^{3}

\newline

Answer:

Evaluate at $x = 0$ : To find the $y$ -coordinate of the $y$ -intercept of the polynomial function $f(x)$ , we need to evaluate the function at $x = 0$ . This is because the $y$ -intercept occurs where the graph of the function crosses the $y$ -axis, and the $x$ -coordinate of any point on the $y$ -axis is $0$ .
Substitute $x = 0$ : Substitute $x = 0$ into the function $f(x) = -x(x - 3)(x^2 + 2)^3$ . $\newline$ $f(0) = -0(0 - 3)(0^2 + 2)^3$
Simplify expression: Simplify the expression by performing the operations. $\newline$ $f(0) = -0 \times (-3) \times (0 + 2)^3$ $\newline$ $f(0) = 0 \times 3 \times 2^3$ $\newline$ $f(0) = 0 \times 3 \times 8$ $\newline$ $f(0) = 0$
Final result: Since the result of $f(0)$ is $0$ , the $y$ -coordinate of the $y$ -intercept of the polynomial function $f(x)$ is $0$ .

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