High School

Perform the indicated operations:

\[ (9x^5 + 4x^3 + 8x) + (8x^5 + 9x^3 + 7x) \]

Choose the correct result:

A. \[ 45x^9 \]
B. \[ 17x + 13x^5 + 15x^3 \]
C. \[ 16x^5 + 18x^3 + 11x \]
D. \[ 17x^5 + 13x^3 + 15x \]

Answer :

To solve the problem, we need to add the two polynomial expressions:

1. First Polynomial: [tex]\(9x^5 + 4x^3 + 8x\)[/tex]
2. Second Polynomial: [tex]\(8x^5 + 9x^3 + 7x\)[/tex]

Let's perform the addition step-by-step:

Step 1: Add the [tex]\(x^5\)[/tex] terms.

- From the first polynomial, the coefficient of [tex]\(x^5\)[/tex] is 9.
- From the second polynomial, the coefficient of [tex]\(x^5\)[/tex] is 8.
- Sum: [tex]\(9 + 8 = 17\)[/tex]

So, the term for [tex]\(x^5\)[/tex] in the result is [tex]\(17x^5\)[/tex].

Step 2: Add the [tex]\(x^3\)[/tex] terms.

- From the first polynomial, the coefficient of [tex]\(x^3\)[/tex] is 4.
- From the second polynomial, the coefficient of [tex]\(x^3\)[/tex] is 9.
- Sum: [tex]\(4 + 9 = 13\)[/tex]

So, the term for [tex]\(x^3\)[/tex] in the result is [tex]\(13x^3\)[/tex].

Step 3: Add the [tex]\(x\)[/tex] terms.

- From the first polynomial, the coefficient of [tex]\(x\)[/tex] is 8.
- From the second polynomial, the coefficient of [tex]\(x\)[/tex] is 7.
- Sum: [tex]\(8 + 7 = 15\)[/tex]

So, the term for [tex]\(x\)[/tex] in the result is [tex]\(15x\)[/tex].

Now, combining all these results, the expression becomes:

[tex]\[ 17x^5 + 13x^3 + 15x \][/tex]

Therefore, the correct option is:
[tex]\[ 17x^5 + 13x^3 + 15x \][/tex]

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