Question

practice: rewrite a rational expression as quotient and remainder
which of the following is equivalent to \\(\dfrac{x^2 + 5x + 2}{x + 5}\\)?

choose 1 answer:

\\(\boldsymbol{\text{a}}\\) \\(x + 1\\)

\\(\boldsymbol{\text{b}}\\) \\(x + 2\\)

\\(\boldsymbol{\text{c}}\\) \\(x + \dfrac{2}{x + 5}\\)

\\(\boldsymbol{\text{d}}\\) \\(x + 1 - \dfrac{4}{x + 5}\\)

check
explain

Explanation:

Step1: Divide the numerator

We perform polynomial long division of \(x^{2}+5x + 2\) by \(x + 5\). First, divide \(x^{2}\) by \(x\) to get \(x\). Multiply \(x+5\) by \(x\) to get \(x^{2}+5x\).

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Step2: Combine the quotient and remainder

The quotient from the division is \(x\) and the remainder is \(2\). So, \(\frac{x^{2}+5x + 2}{x + 5}=x+\frac{2}{x + 5}\)

Answer:

C. \(x+\dfrac{2}{x + 5}\)