Questions: Follow the steps for graphing a rational function to graph the function F(x) = (x^2 + 7x - 8)/(x + 2). If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of F(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. F(x) = (Type your answer in factored form. Do not simplify.) B. F(x) is already in factored form.

Follow the steps for graphing a rational function to graph the function F(x) = (x^2 + 7x - 8)/(x + 2). If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of F(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. F(x) = (Type your answer in factored form. Do not simplify.) B. F(x) is already in factored form.
Transcript text: Follow the steps for graphing a rational function to graph the function $F(x)=\frac{x^{2}+7 x-8}{x+2}$. If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of $F(x)$. Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. $F(x)=$ $\square$ (Type your answer in factored form. Do not simplify.) B. $F(x)$ is already in factored form.
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Solution

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Solution Steps

Step 1: Write the function as a single rational expression

The given function is already a single rational expression: \[ F(x) = \frac{x^2 + 7x - 8}{x + 2} \]

Step 2: Factor the numerator

The numerator \(x^2 + 7x - 8\) can be factored. We need to find two numbers that multiply to \(-8\) and add to \(7\). These numbers are \(8\) and \(-1\). Thus, the numerator factors as: \[ x^2 + 7x - 8 = (x + 8)(x - 1) \]

Step 3: Factor the denominator

The denominator \(x + 2\) is already in its simplest form.

Final Answer

The function in factored form is: \[ F(x) = \frac{(x + 8)(x - 1)}{x + 2} \]

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