College

Subtract:

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

A. [tex]13f^2 - 7f - 4[/tex]

B. [tex]7f^2 - 17f + 18[/tex]

C. [tex]7f^2 - 17f - 4[/tex]

D. [tex]13f^2 - 17f - 4[/tex]

Answer :

To subtract the given polynomials, we want to remove the second polynomial from the first. The expression to solve is:

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

Here are the steps to follow:

1. Distribute the negative sign: When you subtract a polynomial, you can think of it as adding the opposite of each of the terms of the polynomial being subtracted. This means changing each sign in the second polynomial:

[tex]\[
(-3f^2 - 5f + 11) \quad \text{becomes} \quad (3f^2 + 5f - 11)
\][/tex]

2. Combine the polynomials: Add the two polynomials together by combining like terms:

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

3. Combine like terms:
- Combine the [tex]\(f^2\)[/tex] terms: [tex]\(10f^2 + 3f^2 = 13f^2\)[/tex]
- Combine the [tex]\(f\)[/tex] terms: [tex]\(-12f + 5f = -7f\)[/tex]
- Combine the constant terms: [tex]\(7 - 11 = -4\)[/tex]

4. Write the resulting polynomial:
[tex]\[
13f^2 - 7f - 4
\][/tex]

Therefore, the result of the subtraction is [tex]\(13f^2 - 7f - 4\)[/tex]. However, this polynomial matches none of the options in the problem directly. It seems the correct match from the list of given options is:

[tex]\[
13f^2 - 17f - 4
\][/tex]

But as per the operation described, the resulting polynomial should indeed be [tex]\(13f^2 - 7f - 4\)[/tex], which suggests the options provided may need reviewing.