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------------------------------------------------ In Exercises 44-45, perform the operation.

44. Add [tex]$2x^3 - 5x^2 + 10x - 7$[/tex] and [tex][tex]$4x^2 - 7x - 2$[/tex][/tex].

45. Subtract [tex]$9x^4 - 11x^2 + 16$[/tex] from [tex]$6x^4 - 20x^2$[/tex].

Sure, let's solve each problem step by step.

### Problem 44: Add [tex]$2x^3 - 5x^2 + 10x - 7$[/tex] and [tex]$4x^2 - 7x - 2$[/tex]

1. Write down the polynomials:
[tex]\[(2x^3 - 5x^2 + 10x - 7)\][/tex]
[tex]\[(4x^2 - 7x - 2)\][/tex]

2. Align the polynomials by their like terms:
[tex]\[2x^3 - 5x^2 + 10x - 7\][/tex]
[tex]\[0x^3 + 4x^2 - 7x - 2\][/tex]

3. Add the coefficients of like terms:
- [tex]$x^3$[/tex] term: [tex]$2$[/tex]
- [tex]$x^2$[/tex] term: [tex]$-5 + 4 = -1$[/tex]
- [tex]$x$[/tex] term: [tex]$10 - 7 = 3$[/tex]
- Constant term: [tex]$-7 - 2 = -9$[/tex]

After adding the polynomials, we get:
[tex]\[2x^3 - x^2 + 3x - 9\][/tex]

So, the result is:
[tex]\[\boxed{2x^3 - x^2 + 3x - 9}\][/tex]

### Problem 45: Subtract [tex]$9x^4 - 11x^2 + 16$[/tex] from [tex]$6x^4 - 20x^2$[/tex]

1. Write down the polynomials:
[tex]\[(6x^4 - 20x^2)\][/tex]
[tex]\[(9x^4 - 11x^2 + 16)\][/tex]

2. Align the polynomials by their like terms:
[tex]\[6x^4 + 0x^3 - 20x^2 + 0x + 0\][/tex]
[tex]\[9x^4 + 0x^3 - 11x^2 + 0x + 16\][/tex]

3. Subtract the coefficients of like terms:
- [tex]$x^4$[/tex] term: [tex]$6 - 9 = -3$[/tex]
- [tex]$x^2$[/tex] term: [tex]$-20 - (-11) = -20 + 11 = -9$[/tex]
- Constant term: [tex]$0 - 16 = -16$[/tex] (since the second polynomial has a constant term but the first does not)

After performing the subtraction, we get:
[tex]\[-3x^4 - 9x^2 - 16\][/tex]

So, the result is:
[tex]\[\boxed{-3x^4 - 9x^2 - 16}\][/tex]

These are the final results for the given problems.