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.
[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.
