Alright, let's classify and combine the like terms for each of the given polynomials step-by-step:
### 1. Polynomial: [tex]\( 2x - x^2 + 4x + x^2 \)[/tex]
Combine the like terms:
- [tex]\( 2x + 4x = 6x \)[/tex]
- [tex]\(-x^2 + x^2 = 0\)[/tex]
Thus, the combined polynomial is:
[tex]\[ 6x \][/tex]
### 2. Polynomial: [tex]\( x^3 - 5x^2 + 3 - 2 \)[/tex]
Combine the like terms:
- [tex]\( 3 - 2 = 1 \)[/tex]
So, the combined polynomial is:
[tex]\[ x^3 - 5x^2 + 1 \][/tex]
### 3. Polynomial: [tex]\( x^3 - x^3 + x^2 - x^2 + 3 \)[/tex]
Combine the like terms:
- [tex]\( x^3 - x^3 = 0 \)[/tex]
- [tex]\( x^2 - x^2 = 0 \)[/tex]
So, the combined polynomial is:
[tex]\[ 3 \][/tex]
### 4. Polynomial: [tex]\( 7x - x^2 + x^3 + 4x^2 \)[/tex]
Combine the like terms:
- [tex]\(-x^2 + 4x^2 = 3x^2\)[/tex]
So, the combined polynomial is:
[tex]\[ x^3 + 3x^2 + 7x \][/tex]
### 5. Polynomial: [tex]\( -6x - x^3 + 6x - 4x \)[/tex]
Combine the like terms:
- [tex]\(-6x + 6x - 4x = -4x\)[/tex]
So, the combined polynomial is:
[tex]\[ -x^3 - 4x \][/tex]
### Final Results:
Let's summarize each combined polynomial:
1. [tex]\( 6x \)[/tex]
2. [tex]\( x^3 - 5x^2 + 1 \)[/tex]
3. [tex]\( 3 \)[/tex]
4. [tex]\( x^3 + 3x^2 + 7x \)[/tex]
5. [tex]\( -x^3 - 4x \)[/tex]
Each polynomial is now simplified and classified based on combining the like terms effectively.
