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Answer :
Let's add the polynomials step-by-step.
We are given the expression:
[tex]\[
\begin{array}{r}
2x^7 + 5x + 4 \\
+\quad 5x^9 + 8x \\
\hline
\end{array}
\][/tex]
To add these polynomials, we combine like terms, which are terms with the same power of [tex]\(x\)[/tex].
Let's identify and combine each set of like terms:
1. Terms with [tex]\(x^9\)[/tex]:
- The only [tex]\(x^9\)[/tex] term is from the second polynomial: [tex]\(5x^9\)[/tex].
2. Terms with [tex]\(x^7\)[/tex]:
- The only [tex]\(x^7\)[/tex] term is from the first polynomial: [tex]\(2x^7\)[/tex].
3. Terms with [tex]\(x\)[/tex]:
- From the first polynomial, we have [tex]\(5x\)[/tex].
- From the second polynomial, we have [tex]\(8x\)[/tex].
- Adding these gives us [tex]\(5x + 8x = 13x\)[/tex].
4. Constant terms:
- The constant term from the first polynomial is [tex]\(4\)[/tex].
- There is no constant term in the second polynomial.
- Therefore, the constant term in the sum is [tex]\(4\)[/tex].
Putting all these together, the sum of the polynomials is:
[tex]\[ 5x^9 + 2x^7 + 13x + 4 \][/tex]
Thus, the polynomial that represents the sum is:
D. [tex]\(5x^9 + 2x^7 + 13x + 4\)[/tex]
We are given the expression:
[tex]\[
\begin{array}{r}
2x^7 + 5x + 4 \\
+\quad 5x^9 + 8x \\
\hline
\end{array}
\][/tex]
To add these polynomials, we combine like terms, which are terms with the same power of [tex]\(x\)[/tex].
Let's identify and combine each set of like terms:
1. Terms with [tex]\(x^9\)[/tex]:
- The only [tex]\(x^9\)[/tex] term is from the second polynomial: [tex]\(5x^9\)[/tex].
2. Terms with [tex]\(x^7\)[/tex]:
- The only [tex]\(x^7\)[/tex] term is from the first polynomial: [tex]\(2x^7\)[/tex].
3. Terms with [tex]\(x\)[/tex]:
- From the first polynomial, we have [tex]\(5x\)[/tex].
- From the second polynomial, we have [tex]\(8x\)[/tex].
- Adding these gives us [tex]\(5x + 8x = 13x\)[/tex].
4. Constant terms:
- The constant term from the first polynomial is [tex]\(4\)[/tex].
- There is no constant term in the second polynomial.
- Therefore, the constant term in the sum is [tex]\(4\)[/tex].
Putting all these together, the sum of the polynomials is:
[tex]\[ 5x^9 + 2x^7 + 13x + 4 \][/tex]
Thus, the polynomial that represents the sum is:
D. [tex]\(5x^9 + 2x^7 + 13x + 4\)[/tex]
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