To add the polynomials, combine like terms:

(4x² - 3x + 2) + (3x² + 2x - 1)

Combine the x² terms, x terms, and the constant terms:

4x² + 3x² - 3x + 2x + 2 - 1

Simplify:

7x² - x + 1

To factor the polynomial, find two binomials whose product gives the original polynomial:

6x² - 7x - 20

First, find two numbers that multiply to give the product of the leading coefficient (6) and the constant (-20), which is -120.

The two numbers that multiply to give -120 and add to give the middle term coefficient (-7) are -15 and 8.

Now, rewrite the polynomial, replacing the middle term with the sum -15x + 8x:

6x² - 15x + 8x - 20

Factor by grouping:

3x(2x - 5) + 4(2x - 5)

Both expressions in parentheses are the same, so factor it out:

(2x - 5)(3x + 4)

To find the sum, first find a common denominator. In this case, the common denominator is (x + 1)(x - 1).

Next, rewrite each fraction with the common denominator:

(3x² + 4x - 2)(x - 1)/((x + 1)(x - 1)) + (2x + 3)(x + 1)/((x + 1)(x - 1))

Now, add the two fractions:

[(3x² + 4x - 2)(x - 1) + (2x + 3)(x + 1)]/((x + 1)(x - 1))

Expand the numerators:

[(3x³ - 3x² + 1x - 4x² + 4x - 2) + (2x² + 5x + 3)]/((x + 1)(x - 1))

Combine like terms in the numerator:

[3x³ - 7x² + 5x - 2]/((x + 1)(x - 1))

To simplify the expression, add the like terms:

(6x² - 9x + 4) + (2x² - x - 2)

Combine the x² terms, x terms, and constant terms:

6x² + 2x² - 9x - x + 4 - 2

Simplify:

8x² - 10x + 2

To subtract the polynomials, subtract the like terms:

(6x² - x + 4) - (3x² - 2x - 2)

Subtract the x² terms, x terms, and constant terms:

6x² - 3x² - x + 2x + 4 + 2

Simplify:

3x² + x + 6