Question

rewrite the following polynomial in standard form. 1 + \frac{x^{3}}{6} + 5x

Explanation:

Step1: Recall standard form of polynomial

The standard form of a polynomial is to write the terms in descending order of their exponents. The general form for a cubic polynomial (degree 3) is \(ax^{3}+bx^{2}+cx + d\), where \(a
eq0\) and the exponents of \(x\) are in decreasing order.

Step2: Identify the terms and their degrees

• The term \(\frac{x^{3}}{6}\) has a degree of 3.
• The term \(5x\) has a degree of 1.
• The term \(1\) (which can be written as \(1x^{0}\)) has a degree of 0.
• There is no \(x^{2}\) term, so its coefficient is 0.

Step3: Arrange the terms in descending order of degrees

Arrange the terms from the highest degree to the lowest degree. So we have the \(x^{3}\) term first, then the \(x^{2}\) term (which is \(0x^{2}\), but we can omit it since its coefficient is 0), then the \(x\) term, and then the constant term.

So the polynomial \(1+\frac{x^{3}}{6}+5x\) in standard form is \(\frac{x^{3}}{6}+0x^{2}+5x + 1\), or simply \(\frac{x^{3}}{6}+5x + 1\) (since the \(x^{2}\) term with coefficient 0 does not affect the polynomial).

Answer:

\(\frac{x^{3}}{6}+5x + 1\)