Question

rewrite the following polynomial in standard form.
\\(\frac{x^3}{5} - 10 - x\\)

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written in descending order of the exponents of the variable. The general form for a cubic polynomial (degree 3) is \(ax^{3}+bx^{2}+cx + d\), where \(a
eq0\), and \(a,b,c,d\) are constants.

Step2: Rearrange the given polynomial

The given polynomial is \(\frac{x^{3}}{5}-10 - x\). We need to arrange the terms in descending order of the exponent of \(x\).

• The term with \(x^{3}\) is \(\frac{x^{3}}{5}\) (exponent 3).
• The term with \(x^{2}\): there is no \(x^{2}\) term, so its coefficient is 0, so we can write \(0x^{2}\) (but usually we can omit the term with coefficient 0 if we want, but to show the standard form clearly, we can include it or not. However, the key is descending order of exponents).
• The term with \(x\) is \(-x\) (exponent 1).
• The constant term is \(- 10\) (exponent 0).

So rearranging in descending order of exponents: \(\frac{x^{3}}{5}+0x^{2}-x - 10\). Since the \(x^{2}\) term has a coefficient of 0, we can also write it as \(\frac{1}{5}x^{3}-x - 10\).

Answer:

\(\frac{1}{5}x^{3}-x - 10\) (or \(\frac{x^{3}}{5}+0x^{2}-x - 10\))