College

Select all polynomial expressions that are equivalent to [tex]6x^4 + 4x^3 - 7x^2 + 5x + 8[/tex].

A. [tex]16x^{10}[/tex]

B. [tex]6x^5 + 4x^4 - 7x^3 + 5x^2 + 8x[/tex]

C. [tex]6x^4 + 4x^3 - 7x^2 + 5x + 8[/tex]

D. [tex]8 + 5x + 7x^2 - 4x^3 + 6x^4[/tex]

E. [tex]8 + 5x - 7x^2 + 4x^3 + 6x^4[/tex]

Answer :

Answer:

C and E

Step-by-step explanation:

Given

[tex]Polynomial: 6x^4 + 4x^3 - 7x^2 + 5x + 8.[/tex]

Required

Select all equivalent polynomial

Scanning through the given options;

[tex]A:\ 16x^{10}[/tex]

This is not equivalent because the degree of the polynomial begins from 10.

[tex]B: 6x^5+ 4x^4 - 7x^3 +5x^2+ 8x[/tex]

This is not equivalent because the degree of the polynomial begins from 5.

[tex]C: 6x^4+ 4x^3 - 7x^2 + 5x + 8[/tex]

Compare this to the given polynomial; They are equivalent

[tex]Polynomial: 6x^4 + 4x^3 - 7x^2 + 5x + 8.[/tex]

[tex]D: 8 + 5x + 7x^2 - 4x^3+ 6x^4[/tex]

Reorder

[tex]D:\ 6x^4- 4x^3+ 7x^2+ 5x +8[/tex]

Compare this to the given polynomial; They are not equivalent because of the difference in sign in front of [tex]7x^2[/tex]

[tex]E:\ 8 + 5x - 7x\² + 4x^3+ 6x^4[/tex]

Reorder

[tex]Polynomial: 6x^4 + 4x^3 - 7x^2 + 5x + 8.[/tex]

Compare this to the given polynomial; They are equivalent

[tex]Polynomial: 6x^4 + 4x^3 - 7x^2 + 5x + 8.[/tex]

Hence:

Option C and E answers the question