Answer :
To solve the problem, we need to add the two polynomials:
[tex]$$3x^6 + 7x + 3 \quad \text{and} \quad 5x^9 + 12x.$$[/tex]
Step 1. Write both polynomials with like terms:
- The first polynomial can be written as:
[tex]$$0x^9 + 3x^6 + 7x + 3.$$[/tex]
- The second polynomial can be written as:
[tex]$$5x^9 + 0x^6 + 12x + 0.$$[/tex]
Step 2. Add the corresponding coefficients:
- For the [tex]$x^9$[/tex] term:
[tex]$$0 + 5 = 5,$$[/tex]
so we have [tex]$5x^9$[/tex].
- For the [tex]$x^6$[/tex] term:
[tex]$$3 + 0 = 3,$$[/tex]
so we have [tex]$3x^6$[/tex].
- For the [tex]$x^1$[/tex] term:
[tex]$$7 + 12 = 19,$$[/tex]
so we have [tex]$19x$[/tex].
- For the constant term:
[tex]$$3 + 0 = 3,$$[/tex]
so we have [tex]$3$[/tex].
Step 3. Write the resulting polynomial:
[tex]$$5x^9 + 3x^6 + 19x + 3.$$[/tex]
Comparing this result to the multiple-choice options, we see that it corresponds to option C.
[tex]$$3x^6 + 7x + 3 \quad \text{and} \quad 5x^9 + 12x.$$[/tex]
Step 1. Write both polynomials with like terms:
- The first polynomial can be written as:
[tex]$$0x^9 + 3x^6 + 7x + 3.$$[/tex]
- The second polynomial can be written as:
[tex]$$5x^9 + 0x^6 + 12x + 0.$$[/tex]
Step 2. Add the corresponding coefficients:
- For the [tex]$x^9$[/tex] term:
[tex]$$0 + 5 = 5,$$[/tex]
so we have [tex]$5x^9$[/tex].
- For the [tex]$x^6$[/tex] term:
[tex]$$3 + 0 = 3,$$[/tex]
so we have [tex]$3x^6$[/tex].
- For the [tex]$x^1$[/tex] term:
[tex]$$7 + 12 = 19,$$[/tex]
so we have [tex]$19x$[/tex].
- For the constant term:
[tex]$$3 + 0 = 3,$$[/tex]
so we have [tex]$3$[/tex].
Step 3. Write the resulting polynomial:
[tex]$$5x^9 + 3x^6 + 19x + 3.$$[/tex]
Comparing this result to the multiple-choice options, we see that it corresponds to option C.
