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Answer :
Sure! Let's find the polynomial that represents the sum of the given expressions step-by-step:
To find the sum of the two polynomials, we need to add the coefficients of like terms together. The polynomials given are:
1. [tex]\(2x^7 + 5x + 4\)[/tex]
2. [tex]\(5x^8 + 8x\)[/tex]
Step 1: Align the polynomials by their degree terms.
[tex]\[
\begin{array}{r}
2x^7 + 0x^6 + 0x^5 + 0x^4 + 0x^3 + 0x^2 + 5x + 4 \\
+ \quad 5x^8 + 0x^7 + 0x^6 + 0x^5 + 0x^4 + 0x^3 + 8x \\
\hline
\end{array}
\][/tex]
Step 2: Add the coefficients of like terms.
- For [tex]\(x^8\)[/tex], we have no term in the first polynomial, so the result is [tex]\(5x^8\)[/tex].
- For [tex]\(x^7\)[/tex], we have [tex]\(2x^7\)[/tex].
- For [tex]\(x^6\)[/tex], [tex]\(x^5\)[/tex], [tex]\(x^4\)[/tex], [tex]\(x^3\)[/tex], and [tex]\(x^2\)[/tex], there are no terms in both polynomials, so they remain [tex]\(0\)[/tex].
- For [tex]\(x\)[/tex], add [tex]\(5x\)[/tex] from the first polynomial and [tex]\(8x\)[/tex] from the second polynomial to get [tex]\(13x\)[/tex].
- For the constant term: [tex]\(4\)[/tex] from the first polynomial since there is no constant in the second one.
Putting it together, the sum is:
[tex]\[
5x^8 + 2x^7 + 13x + 4
\][/tex]
Therefore, the polynomial representing the sum is [tex]\(5x^8 + 2x^7 + 13x + 4\)[/tex].
Unfortunately, this specific polynomial doesn't exactly match with any given options, but we should verify with the closest matching option from the list, if applicable.
Note: If provided choices differ, you should check for errors in those options accordingly.
To find the sum of the two polynomials, we need to add the coefficients of like terms together. The polynomials given are:
1. [tex]\(2x^7 + 5x + 4\)[/tex]
2. [tex]\(5x^8 + 8x\)[/tex]
Step 1: Align the polynomials by their degree terms.
[tex]\[
\begin{array}{r}
2x^7 + 0x^6 + 0x^5 + 0x^4 + 0x^3 + 0x^2 + 5x + 4 \\
+ \quad 5x^8 + 0x^7 + 0x^6 + 0x^5 + 0x^4 + 0x^3 + 8x \\
\hline
\end{array}
\][/tex]
Step 2: Add the coefficients of like terms.
- For [tex]\(x^8\)[/tex], we have no term in the first polynomial, so the result is [tex]\(5x^8\)[/tex].
- For [tex]\(x^7\)[/tex], we have [tex]\(2x^7\)[/tex].
- For [tex]\(x^6\)[/tex], [tex]\(x^5\)[/tex], [tex]\(x^4\)[/tex], [tex]\(x^3\)[/tex], and [tex]\(x^2\)[/tex], there are no terms in both polynomials, so they remain [tex]\(0\)[/tex].
- For [tex]\(x\)[/tex], add [tex]\(5x\)[/tex] from the first polynomial and [tex]\(8x\)[/tex] from the second polynomial to get [tex]\(13x\)[/tex].
- For the constant term: [tex]\(4\)[/tex] from the first polynomial since there is no constant in the second one.
Putting it together, the sum is:
[tex]\[
5x^8 + 2x^7 + 13x + 4
\][/tex]
Therefore, the polynomial representing the sum is [tex]\(5x^8 + 2x^7 + 13x + 4\)[/tex].
Unfortunately, this specific polynomial doesn't exactly match with any given options, but we should verify with the closest matching option from the list, if applicable.
Note: If provided choices differ, you should check for errors in those options accordingly.
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