Answer:
[tex]- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{4} - 2x^5 + \frac{x^3}{2} + 1[/tex]
Required
The standard form of the polynomial
The general form of a polynomial is
[tex]ax^n + bx^{n-1} + cx^{n-2} +........+ k[/tex]
Where k is a constant and the terms are arranged from biggest to smallest exponents
We start by rearranging the given polynomial
[tex]- 2x^5+ \frac{x^3}{2} +\frac{x}{4} + 1[/tex]
Given that the highest exponent of x is 5;
Let n = 5
Then we fix in the missing terms in terms of n
[tex]- 2x^5+ 0x^{n-1} + \frac{x^3}{2} +0x^{n-3}+\frac{x}{4} + 1[/tex]
Substitute 5 for n
[tex]- 2x^5+ 0x^{5-1} + \frac{x^3}{2} +0x^{5-3}+\frac{x}{4} + 1[/tex]
[tex]- 2x^5+ 0x^{4} + \frac{x^3}{2} +0x^{2}+\frac{x}{4} + 1[/tex]
Hence, the standard form of the given polynomial is [tex]- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1[/tex]
