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]
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]
