College

Subtract:

[tex]\left(10f^2 - 12f + 7\right) - \left(-3f^2 - 5f + 11\right)[/tex]

A. [tex]13f^2 - 17f - 4[/tex]
B. [tex]13f^2 - 7f - 4[/tex]
C. [tex]7f^2 - 17f - 4[/tex]
D. [tex]7f^2 - 17f + 18[/tex]

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]