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

Its B

Explanation:

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Answer 2

`- 2x^5+ 0x^4 + (x^3)/(2) +0x^2+(x)/(4) + 1`

Explanation:

Given

`(x)/(4) - 2x^5 + (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+ (x^3)/(2) +(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) + (x^3)/(2) +0x^(n-3)+(x)/(4) + 1`

Substitute 5 for n

`- 2x^5+ 0x^(5-1) + (x^3)/(2) +0x^(5-3)+(x)/(4) + 1`

`- 2x^5+ 0x^(4) + (x^3)/(2) +0x^(2)+(x)/(4) + 1`

Hence, the standard form of the given polynomial is
`- 2x^5+ 0x^4 + (x^3)/(2) +0x^2+(x)/(4) + 1`