Answer :
We start with the two polynomials:
[tex]$$
4x^3 + 6x - 7 \quad \text{and} \quad 3x^3 - 5x^2 - 5x.
$$[/tex]
Our goal is to add these expressions together. Follow these steps:
1. Group the like terms.
Identify the terms with the same power of [tex]$x$[/tex]:
- The [tex]$x^3$[/tex] terms are [tex]$4x^3$[/tex] and [tex]$3x^3$[/tex].
- The [tex]$x^2$[/tex] term is [tex]$-5x^2$[/tex] (note that the first polynomial does not contain an [tex]$x^2$[/tex] term).
- The [tex]$x$[/tex] terms are [tex]$6x$[/tex] and [tex]$-5x$[/tex].
- The constant term is [tex]$-7$[/tex].
2. Add the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 + 3x^3 = 7x^3.
$$[/tex]
3. Add the [tex]$x^2$[/tex] terms:
[tex]$$
0 - 5x^2 = -5x^2.
$$[/tex]
4. Add the [tex]$x$[/tex] terms:
[tex]$$
6x - 5x = x.
$$[/tex]
5. Write down the constant term:
[tex]$$
-7.
$$[/tex]
6. Combine all the results:
The sum of the polynomials is
[tex]$$
7x^3 - 5x^2 + x - 7.
$$[/tex]
Among the provided choices, the expression that matches our result is:
[tex]$$
7x^3 - 5x^2 + x - 7.
$$[/tex]
This corresponds to the second option.
[tex]$$
4x^3 + 6x - 7 \quad \text{and} \quad 3x^3 - 5x^2 - 5x.
$$[/tex]
Our goal is to add these expressions together. Follow these steps:
1. Group the like terms.
Identify the terms with the same power of [tex]$x$[/tex]:
- The [tex]$x^3$[/tex] terms are [tex]$4x^3$[/tex] and [tex]$3x^3$[/tex].
- The [tex]$x^2$[/tex] term is [tex]$-5x^2$[/tex] (note that the first polynomial does not contain an [tex]$x^2$[/tex] term).
- The [tex]$x$[/tex] terms are [tex]$6x$[/tex] and [tex]$-5x$[/tex].
- The constant term is [tex]$-7$[/tex].
2. Add the [tex]$x^3$[/tex] terms:
[tex]$$
4x^3 + 3x^3 = 7x^3.
$$[/tex]
3. Add the [tex]$x^2$[/tex] terms:
[tex]$$
0 - 5x^2 = -5x^2.
$$[/tex]
4. Add the [tex]$x$[/tex] terms:
[tex]$$
6x - 5x = x.
$$[/tex]
5. Write down the constant term:
[tex]$$
-7.
$$[/tex]
6. Combine all the results:
The sum of the polynomials is
[tex]$$
7x^3 - 5x^2 + x - 7.
$$[/tex]
Among the provided choices, the expression that matches our result is:
[tex]$$
7x^3 - 5x^2 + x - 7.
$$[/tex]
This corresponds to the second option.
