High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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]