(35x³+41x²+13x-5):(5x-2)

a) To divide (35x³+41x²+13x-5) by (5x-2), we can use long division:

7x² + 11x + 6
---------------------
5x - 2 | 35x³ + 41x² + 13x - 5
- (35x³ - 14x²)
-----------------
55x² + 13x
- (55x² - 22x)
----------------
35x - 5
- (35x - 14)
-------------
9

Therefore, the result is 7x² + 11x + 6 with a remainder of 9.

b) The expression x⁴-6x³+16x²-22x+15 cannot be divided by any linear expression (in the form ax+b) since the degree of the divisor is 1 and the degree of the dividend is 4. Therefore, this expression cannot be divided further.

c) To divide (3x⁴-8x³-10x²+8x-5) by (3x²-2x+1), we can use long division:

x² - 2x - 3
---------------------
3x² - 2x + 1 | 3x⁴ - 8x³ - 10x² + 8x - 5
- (3x⁴ - 2x³ + x²)
---------------------
-6x³ - 11x² + 8x
+ (6x³ - 4x² + 2x)
-------------------
-15x² + 10x - 5
+ (15x² - 10x + 5)
-----------------
0

Therefore, the result is x² - 2x - 3 with no remainder.

d) To divide (2x³-9x²+19x-15) by (x²-3x+5), we can use long division:

2x - 3
---------------------
x² - 3x + 5 | 2x³ - 9x² + 19x - 15
- (2x³ - 6x² + 10x)
-------------------
-3x² + 9x - 15
+ (3x² - 9x + 15)
----------------
0

Therefore, the result is 2x - 3 with no remainder.

e) To divide (15x⁴-x³-x²+41x-70) by (3x²-2x+7), we can use long division:

5x² + 4x - 10
---------------------
3x² - 2x + 7 | 15x⁴ - x³ - x² + 41x - 70
- (15x⁴ - 10x³ + 35x²)
-----------------------
9x³ - 36x² + 41x - 70
- (9x³ - 6x² + 21x)
-------------------
-30x² + 20x - 70
+ (30x² - 20x + 70)
-----------------
0

Therefore, the result is 5x² + 4x - 10 with no remainder.