Question

1) Sendo P(x) = 5X³ + 3X² - 5X + 8 e Q (x) = X³ + 2X² - x + 8 calcule:
A) p(x) + Q (x)

B) p(x) - Q (x)

c) Q (x) + p(x)

D) Q(x) - P(x)

Answer 1

$P(x) = 5x^3 + 3x^2 -5x + 8 \\ \\ Q(x) = x^3 + 2x^2 - x + 8$

$A) P(x) + Q(x) \\ \\ \\ 5x^3 + 3x^2 -5x + 8 + x^3 + 2x^2 - x + 8 \\ \\ \\ 5x^3 + x^3 + 3x^2 + 2x^2 - 5x - x + 8 + 8 \\ \\ \\ => 6x^3 + 5x^2 - 6x + 16$

==============

$B) P(x) - Q(x) = 5x^3 + 3x^2 -5x + 8 - (x^3 + 2x^2 - x + 8) \\ \\ \\ 5x^3 + 3x^2 - 5x + 8 -x^3 - 2x^2 + x - 8 \\ \\ \\ => 4x^3 + x^2 - 4x$

==============

$C) Q(x) + p(x) = x^3 + 2x^2 - x + 8 + (5x^3 + 3x^2 -5x + 8) \\ \\ \\ x^3 + 5x^3 + 2x^2 + 3x^2 - x - 5x + 8 + 8 \\ \\ \\ => 6x^3 + 5x^2 - 6x + 16$

==============

$D) Q(x) - P(x) = x^3 + 2x^2 - x + 8 - (5x^3 + 3x^2 -5x + 8) \\ \\ \\ x^3 + 2x^2 - x + 8 - 5x^3 - 3x^2 + 5x - 8 \\ \\ \\ => -4x^3 - x^2 + 4x$