To solve this problem, we need to follow two main subtraction steps with polynomials.
Step 1: Subtract [tex]\(3x^2 + 4x - 5\)[/tex] from [tex]\(7x^2 + x + 9\)[/tex]
Start with the first polynomial:
[tex]\[7x^2 + x + 9\][/tex]
Subtract the second polynomial:
[tex]\[3x^2 + 4x - 5\][/tex]
Combining like terms we get:
[tex]\[
(7x^2 - 3x^2) + (x - 4x) + (9 - (-5))
\][/tex]
[tex]\[
= 4x^2 - 3x + 14
\][/tex]
So, after the first subtraction, the resulting polynomial is:
[tex]\[4x^2 - 3x + 14\][/tex]
Step 2: Subtract [tex]\(4x^2 - 3x\)[/tex] from the resulting polynomial [tex]\(4x^2 - 3x + 14\)[/tex]
Take the resulting polynomial from Step 1:
[tex]\[4x^2 - 3x + 14\][/tex]
Subtract the third polynomial:
[tex]\[4x^2 - 3x\][/tex]
Combining like terms we get:
[tex]\[
(4x^2 - 4x^2) + (-3x - (-3x)) + (14 - 0)
\][/tex]
[tex]\[
= 0x^2 + 0x + 14
\][/tex]
[tex]\[
= 14
\][/tex]
Thus, the final difference after subtracting [tex]\(4x^2 - 3x\)[/tex] from the resulting polynomial is:
[tex]\[14\][/tex]
So, the correct answer is:
[tex]\[14\][/tex]
