Question

1. Select all polynomial expressions that are equivalent to 6x4 + 4x2 – 7x² + 5x + 8.

A. 16x10
B. 6x5 + 4x4 – 7x3 + 5x² + 8x
C. 6x4 + 4x3 - 7x2 + 5x + 8
D. 8 + 5x + 7x2 - 4x3 + 6x4
E. 8 + 5x – 7x2 + 4x3 + 6x4

Answer 1

Options (C) and (E)

Explanation:

Given polynomial is,

6x⁴+ 4x³- 7x² + 5x + 8

So all the polynomials which are (look alike) similar in terms of degree and number of terms to the given expression will be equivalent.

Option (A).

`16x^(10)`

It's a monomial. So not the answer.

Option (B).

6x⁵ + 4x⁴ - 7x³ + 5x² + 8

This polynomial is a 5th degree polynomial, will not be equivalent to the given polynomial expression with 4 degree.

Option (C).

6x⁴ + 4x³ - 7x² + 5x + 8

All the terms and signs between the terms of this expression are similar to the given polynomial expression,

Expression will be equivalent to the given polynomial expression.

Option (D)

8 + 5x + 7x² - 4x³ + 6x⁴

= 6x⁴- 4x³ + 7x² + 5x + 8

Both are similar in number of terms and degree but signs between the terms are different.

Therefore, both the expressions are will not be equivalent.

Option (E).

8 + 5x - 7x² + 4x³ + 6x⁴

= 6x⁴ + 4x³ - 7x² + 5x + 8

Since, both the polynomials are similar so they are equivalent.