Find the sum: (3x² + 5x - 8) + (5x² - 13x - 5)

Solution:

The sum of the two polynomials is done by g the grouping the terms having the same powers of the variable x i.e. x 2 , x etc. Therefore we can write

Sum = (3x² + 5x - 8) + (5x² - 13x - 5)

= (3x² + 5x²) + (5x - 13x) + (-8 - 5)

= 8x² - 8x - 13

Similarly two polynomials like f(x) = 2x⁶ +7x⁵ + 4x⁴ + 3x³ + 5x² + 11x - 9 and g(x) = 5x⁶ + 8x⁵ + 25x⁴ + 13x³ + 9x² + 12 will be added in the manner below:

f(x) + g(x) = (2x⁶ + 5x⁶) + (7x⁵ + 8x⁵) + (4x⁴ + 25x⁴)+ (3x³ + 13x³) + (5x² + 9x²) + (11x) + (-9 + 12)

= 7x⁶ + 15x⁵ + 29x⁴ + 16x³ + 14x² + 11x + 3