Question

answer
$f(x)=(x + 8)(x + 3)(x - 4)$ $f(x)=(x - 8)(x + 3)(x - 4)$
$f(x)=(x + 8)(x - 3)(x + 4)$ $f(x)=(x - 8)(x + 3)(x + 4)$
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Explanation:

Step1: Recall zero - product property

The zeros of a polynomial \(y = f(x)\) are the \(x\) - values for which \(f(x)=0\). If \(f(x)=(x - a)(x - b)(x - c)\), then the zeros are \(x=a\), \(x = b\), and \(x=c\).

Step2: Identify zeros from the graph

The graph of the polynomial intersects the \(x\) - axis at \(x=-8\), \(x=-3\), and \(x = 4\).

Step3: Write the polynomial

Using the zero - product property, if the zeros of the polynomial are \(x=-8\), \(x=-3\), and \(x = 4\), then the polynomial is \(f(x)=(x + 8)(x+3)(x - 4)\).

Answer:

\(f(x)=(x + 8)(x + 3)(x - 4)\)