To subtract the two polynomials [tex]\(\left(3 x^5-2 x^4-5\right)-\left(2 x^4+x^2-10\right)\)[/tex], follow these steps:
1. Write down the two polynomials:
[tex]\[
\text{Poly1} = 3x^5 - 2x^4 - 5
\][/tex]
[tex]\[
\text{Poly2} = 2x^4 + x^2 - 10
\][/tex]
2. Set up the subtraction of the second polynomial from the first:
[tex]\[
3x^5 - 2x^4 - 5 - \left(2x^4 + x^2 - 10\right)
\][/tex]
3. Distribute the negative sign to each term inside the parentheses:
[tex]\[
3x^5 - 2x^4 - 5 - 2x^4 - x^2 + 10
\][/tex]
4. Combine like terms:
- The [tex]\(x^5\)[/tex] term: [tex]\(3x^5\)[/tex]
- The [tex]\(x^4\)[/tex] terms: [tex]\(-2x^4\)[/tex] and [tex]\(-2x^4\)[/tex] combine to [tex]\(-4x^4\)[/tex]
- The [tex]\(x^2\)[/tex] term: [tex]\(-x^2\)[/tex]
- The constant terms: [tex]\(-5\)[/tex] and [tex]\(+10\)[/tex] combine to [tex]\(+5\)[/tex]
5. Write the simplified polynomial:
[tex]\[
3x^5 - 4x^4 - x^2 + 5
\][/tex]
Thus, the correct choice is:
(B) [tex]\(3 x^5 - 4 x^4 - x^2 + 5\)[/tex]
