Let's solve the problem step by step by performing the given polynomial subtractions.
Given polynomials:
1. [tex]\(7x^2 + x + 9\)[/tex]
2. [tex]\(3x^2 + 4x - 5\)[/tex]
3. [tex]\(4x^2 - 3x\)[/tex]
Step 1: Subtract the second polynomial from the first polynomial.
We need to subtract [tex]\(3x^2 + 4x - 5\)[/tex] from [tex]\(7x^2 + x + 9\)[/tex]:
[tex]\[
(7x^2 + x + 9) - (3x^2 + 4x - 5)
\][/tex]
Distribute the negative sign and combine like terms:
[tex]\[
7x^2 + x + 9 - 3x^2 - 4x + 5
\][/tex]
Combine like terms:
[tex]\[
(7x^2 - 3x^2) + (x - 4x) + (9 + 5)
\][/tex]
[tex]\[
4x^2 - 3x + 14
\][/tex]
So, the result of the first subtraction is:
[tex]\[
4x^2 - 3x + 14
\][/tex]
Step 2: Subtract the third polynomial from the result of the first subtraction.
Next, we need to subtract [tex]\(4x^2 - 3x\)[/tex] from [tex]\(4x^2 - 3x + 14\)[/tex]:
[tex]\[
(4x^2 - 3x + 14) - (4x^2 - 3x)
\][/tex]
Distribute the negative sign and combine like terms:
[tex]\[
4x^2 - 3x + 14 - 4x^2 + 3x
\][/tex]
Combine like terms:
[tex]\[
(4x^2 - 4x^2) + (-3x + 3x) + 14
\][/tex]
[tex]\[
0 + 0 + 14
\][/tex]
[tex]\[
14
\][/tex]
So, after performing both subtractions, the final result is:
[tex]\[
\boxed{14}
\][/tex]
