Add (3x⁴ - 2x³ + 1) + (12x⁴ + x² - 11).

Solution:

Given (3x⁴ - 2x³ + 1) + (12x⁴ + x² - 11)

Polynomial addition means adding terms of the same powers of the variable.

Now, put together the terms of same powers

= (3x⁴ +12x⁴) +(-2x³) + (x²) + (1- 11)

= 15x⁴ - 2x³ + x² - 10

Therefore, (3x⁴ - 2x³ + 1) + (12x⁴ + x² - 11) = 15x⁴ - 2x³ + x² - 10

Add (3x⁴ - 2x³ + 1) + (12x⁴ + x² - 11).

Summary:

By adding (3x⁴ - 2x³ + 1) + (12x⁴ + x² - 11) = 15x⁴ - 2x³ + x² - 10.