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Answer :
To solve the subtraction of the polynomials, let's go through the process step-by-step.
We need to subtract two polynomial expressions: [tex]\((10f^2 - 12f + 7) - (-3f^2 - 5f + 11)\)[/tex].
### Step 1: Distribute the Negative Sign
First, distribute the negative sign across the second polynomial:
[tex]\[
-( -3f^2 - 5f + 11) = 3f^2 + 5f - 11
\][/tex]
### Step 2: Combine the Expressions
Now combine this result with the first polynomial:
[tex]\[
(10f^2 - 12f + 7) + (3f^2 + 5f - 11)
\][/tex]
### Step 3: Add the Like Terms Together
Combine like terms:
- [tex]\(f^2\)[/tex] terms: [tex]\(10f^2 + 3f^2 = 13f^2\)[/tex]
- [tex]\(f\)[/tex] terms: [tex]\(-12f + 5f = -7f\)[/tex]
- Constant terms: [tex]\(7 - 11 = -4\)[/tex]
### Step 4: Write the Resulting Polynomial
Putting it all together, the resulting expression is:
[tex]\[
13f^2 - 7f - 4
\][/tex]
This matches one of the answer choices given: [tex]\(13f^2 - 7f - 4\)[/tex].
Therefore, the correct answer is:
[tex]\(13f^2 - 7f - 4\)[/tex]
We need to subtract two polynomial expressions: [tex]\((10f^2 - 12f + 7) - (-3f^2 - 5f + 11)\)[/tex].
### Step 1: Distribute the Negative Sign
First, distribute the negative sign across the second polynomial:
[tex]\[
-( -3f^2 - 5f + 11) = 3f^2 + 5f - 11
\][/tex]
### Step 2: Combine the Expressions
Now combine this result with the first polynomial:
[tex]\[
(10f^2 - 12f + 7) + (3f^2 + 5f - 11)
\][/tex]
### Step 3: Add the Like Terms Together
Combine like terms:
- [tex]\(f^2\)[/tex] terms: [tex]\(10f^2 + 3f^2 = 13f^2\)[/tex]
- [tex]\(f\)[/tex] terms: [tex]\(-12f + 5f = -7f\)[/tex]
- Constant terms: [tex]\(7 - 11 = -4\)[/tex]
### Step 4: Write the Resulting Polynomial
Putting it all together, the resulting expression is:
[tex]\[
13f^2 - 7f - 4
\][/tex]
This matches one of the answer choices given: [tex]\(13f^2 - 7f - 4\)[/tex].
Therefore, the correct answer is:
[tex]\(13f^2 - 7f - 4\)[/tex]
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