Question

Consider the polynomial: StartFraction x Over 4 EndFraction – 2x5 + StartFraction x cubed Over 2 EndFraction + 1 Which polynomial represents the standard form of the original polynomial?

Answer 1

Answer:

$- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1$

Step-by-step explanation:

Given

$\frac{x}{4} - 2x^5 + \frac{x^3}{2} + 1$

Required

The standard form of the polynomial

The general form of a polynomial is

$ax^n + bx^{n-1} + cx^{n-2} +........+ k$

Where k is a constant and the terms are arranged from biggest to smallest exponents

We start by rearranging the given polynomial

$- 2x^5+ \frac{x^3}{2} +\frac{x}{4} + 1$

Given that the highest exponent of x is 5;

Let n = 5

Then we fix in the missing terms in terms of n

$- 2x^5+ 0x^{n-1} + \frac{x^3}{2} +0x^{n-3}+\frac{x}{4} + 1$

Substitute 5 for n

$- 2x^5+ 0x^{5-1} + \frac{x^3}{2} +0x^{5-3}+\frac{x}{4} + 1$

$- 2x^5+ 0x^{4} + \frac{x^3}{2} +0x^{2}+\frac{x}{4} + 1$

Hence, the standard form of the given polynomial is $- 2x^5+ 0x^4 + \frac{x^3}{2} +0x^2+\frac{x}{4} + 1$