Certainly! Let's go through the process step by step to solve the given problem.
We are given two main operations to perform on the polynomials.
1. First Operation: Subtract [tex]\(3x^2 + 4x - 5\)[/tex] from [tex]\(7x^2 + x + 9\)[/tex]
2. Second Operation: Subtract [tex]\(4x^2 - 3x\)[/tex] from the result of the first operation
Let's start with the first operation:
### Step 1: Subtract [tex]\(3x^2 + 4x - 5\)[/tex] from [tex]\(7x^2 + x + 9\)[/tex]
Write down the polynomials:
[tex]\[ 7x^2 + x + 9 \][/tex]
[tex]\[ -(3x^2 + 4x - 5) \][/tex]
To subtract, we change the signs of the second polynomial and then add:
[tex]\[ 7x^2 + x + 9 - (3x^2 + 4x - 5) = 7x^2 + x + 9 - 3x^2 - 4x + 5 \][/tex]
Combine like terms:
[tex]\[ (7x^2 - 3x^2) + (x - 4x) + (9 + 5) \][/tex]
[tex]\[ = 4x^2 - 3x + 14 \][/tex]
So, after the first operation, we are left with the polynomial:
[tex]\[ 4x^2 - 3x + 14 \][/tex]
### Step 2: Subtract [tex]\(4x^2 - 3x\)[/tex] from the result of the first operation:
Write down the polynomials:
[tex]\[ 4x^2 - 3x + 14 \][/tex]
[tex]\[ -(4x^2 - 3x) \][/tex]
Again, change the signs of the second polynomial and then add:
[tex]\[ 4x^2 - 3x + 14 - (4x^2 - 3x) = 4x^2 - 3x + 14 - 4x^2 + 3x \][/tex]
Combine like terms:
[tex]\[ (4x^2 - 4x^2) + (-3x + 3x) + 14 \][/tex]
[tex]\[ = 0 + 0 + 14 \][/tex]
[tex]\[ = 14 \][/tex]
So, after the second operation, we are left with the constant:
[tex]\[ 14 \][/tex]
### Final Results:
- After the first operation: [tex]\(4x^2 - 3x + 14\)[/tex]
- After the second operation: [tex]\(14\)[/tex]
These are the results of the given polynomial operations.
