Question

question
rewrite the following polynomial in standard form.
2 - 9x⁴ - \\(\frac{1}{4}\\)x

Explanation:

Step1: Recall standard form of polynomial

The standard form of a polynomial is to write the terms in descending order of their exponents. For a polynomial in one variable \(x\), the standard form is \(a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_1x + a_0\), where \(a_n
eq0\) and \(n\) is a non - negative integer.

Step2: Identify the exponents of each term

• For the term \(2\), the exponent of \(x\) is \(0\) (since \(2 = 2x^0\)).
• For the term \(- 9x^4\), the exponent of \(x\) is \(4\).
• For the term \(-\frac{1}{4}x\), the exponent of \(x\) is \(1\) (since \(-\frac{1}{4}x=-\frac{1}{4}x^1\)).

Step3: Arrange the terms in descending order of exponents

We arrange the terms from the highest exponent to the lowest exponent. The term with the highest exponent (\(4\)) is \(-9x^4\), then the term with exponent \(1\) is \(-\frac{1}{4}x\), and then the term with exponent \(0\) is \(2\).

So the polynomial in standard form is \(-9x^4-\frac{1}{4}x + 2\).

Answer:

\(-9x^4-\frac{1}{4}x + 2\)