1) To add the two polynomials, we simply add the coefficients of the like terms:

(x² + 3x + 10) + (x + 2) = x² + (3x + x) + (10 + 2)

Combining like terms, we get:

x² + 4x + 12

Therefore, the sum of (x²+3x+10) and (x+2) is x² + 4x + 12.

2) To find the product of (3x²+x-2) and (x-1), we can use the distributive property of multiplication as follows:

(3x²+x-2)(x-1) = 3x²(x-1) + x(x-1) - 2(x-1)

Simplifying each term, we get:

= 3x³ - 3x² + x² - x - 2x + 2

= 3x³ - 2x² - 5x + 2

Therefore, the product of (3x²+x-2) and (x-1) is equal to 3x³ - 2x² - 5x + 2.

3) To add the polynomials (10x² + 4x - 14) and (2x - 2), we simply add the coefficients of the like terms:

(10x² + 4x - 14) + (2x - 2) = 10x² + (4x + 2x) + (-14 - 2)

Simplifying the expression, we get:

= 10x² + 6x - 16

Therefore, the sum of the two polynomials is 10x² + 6x - 16.

4) The expression (32 x²-20x+4) can be factored as follows:

4(8x²-5x+1)

The trinomial 8x²-5x+1 cannot be factored further using integers, so this is the final factored form of the expression

5) To divide (25x²-1) by (5x + 1), we can use long division as follows:5x + 1 | 25x² + 0x - 1

- (25x² + 5x)

__________

-5x - 1

-(-5x - 1)

________

0

Therefore, the quotient is 5x - 1 and the remainder is 0. So we have:

(25x²-1)÷(5x + 1) = 5x - 1