a)
A (x) = 2x³ - 2x + x² - x³ + 3x + 2
= [2x³ + (- x³)] + [( -2x ) + 3x ] + x² + 2
= x³ + x + x² + 2
B(x) = 4x³ - 5x² + 3x - 4x - 3x³ + 4x² + 1
= [4x³ + (- 3x³)] + [(- 5x²) + 4x²] + [3x +(- 4x)] + 1
= x³ + x² + x + 1
b)
A(x) + B(x) = x³ + x + x² + 2 + x³ + x² + x + 1
= ( x³ + x³ )+ ( x + x ) + ( x² + x² ) + ( 2 + 1 )
= 2x³ +2x + 2x² + 3
= 2x³ + 2x² +2x + 3
c)
A(1)= x³ + x + x² + 2
= 1³ + 1+ 1² + 2
= 1 + 1 + 1 + 2
= 5
B (-2)= (-2)³ +(-2)²+ (-2) + 1
= 8 + 4 + (-2) + 1
= 12 + (-1)
= 11