Answer :
Sure, let's carefully go through each polynomial expression provided in the question to see which ones are equivalent to the original polynomial expression [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex].
Given polynomial: [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex]
Now, let's check each option:
A. [tex]\(16x^{10}\)[/tex]
This is a different polynomial with a single term of [tex]\(16x^{10}\)[/tex]. It is not equivalent to our given polynomial.
B. [tex]\(6x^5 + 4x^4 - 7x^3 + 5x^2 + 8x\)[/tex]
This polynomial has different exponents and coefficients compared to our given polynomial. Hence, it is not equivalent.
C. [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex]
This is exactly the same as the given polynomial, so it is indeed equivalent.
D. [tex]\(8 + 5x + 7x^2 - 4x^3 + 6x^4\)[/tex]
To check this polynomial, we need to rewrite it in the standard form (i.e., in descending order of the exponents):
[tex]\[6x^4 - 4x^3 + 7x^2 + 5x + 8\][/tex]
This is not the same as our given polynomial because the coefficients of [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] are different. Thus, it is not equivalent.
E. [tex]\(8 + 5x - 7x^2 + 4x^3 + 6x^4\)[/tex]
Rewrite it in standard form:
[tex]\[6x^4 + 4x^3 - 7x^2 + 5x + 8\][/tex]
This matches the given polynomial exactly, so it is indeed equivalent.
So, the polynomial expressions that are equivalent to [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex] are:
- Option C: [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex]
- Option E: [tex]\(8 + 5x - 7x^2 + 4x^3 + 6x^4\)[/tex]
Therefore, the correct answers are:
C and E
Given polynomial: [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex]
Now, let's check each option:
A. [tex]\(16x^{10}\)[/tex]
This is a different polynomial with a single term of [tex]\(16x^{10}\)[/tex]. It is not equivalent to our given polynomial.
B. [tex]\(6x^5 + 4x^4 - 7x^3 + 5x^2 + 8x\)[/tex]
This polynomial has different exponents and coefficients compared to our given polynomial. Hence, it is not equivalent.
C. [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex]
This is exactly the same as the given polynomial, so it is indeed equivalent.
D. [tex]\(8 + 5x + 7x^2 - 4x^3 + 6x^4\)[/tex]
To check this polynomial, we need to rewrite it in the standard form (i.e., in descending order of the exponents):
[tex]\[6x^4 - 4x^3 + 7x^2 + 5x + 8\][/tex]
This is not the same as our given polynomial because the coefficients of [tex]\(x^3\)[/tex] and [tex]\(x^2\)[/tex] are different. Thus, it is not equivalent.
E. [tex]\(8 + 5x - 7x^2 + 4x^3 + 6x^4\)[/tex]
Rewrite it in standard form:
[tex]\[6x^4 + 4x^3 - 7x^2 + 5x + 8\][/tex]
This matches the given polynomial exactly, so it is indeed equivalent.
So, the polynomial expressions that are equivalent to [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex] are:
- Option C: [tex]\(6x^4 + 4x^3 - 7x^2 + 5x + 8\)[/tex]
- Option E: [tex]\(8 + 5x - 7x^2 + 4x^3 + 6x^4\)[/tex]
Therefore, the correct answers are:
C and E
