Question

2) considere p(x) = 2^4 + 3x² + 4 x +1 , Q (x) = 2x³ + 5x² - x - 3 e G (x) = -2x^4 - 7x² + x - 10 e calcule p grau dos seguintes polinômios:

A) gr [ P(x) + Q(x) - G(x) ] =

B) gr [ P(x) - Q(x) - G(x) ] =

Answer 1

$P(x) = 2x^4 + 3x^2 + 4x + 1 \\ \\ \\ Q(x) = 2x^3 + 5x^2 - x - 3 \\ \\ \\ G(x) = -2x^4 - 7x^2 + x - 10$

a)
gr = [ P(x) + Q(x) - G(x)]

$gr = 2x^4 + 3x^2 + 4x + 1 + (2x^3 + 5x^2 - x - 3)- (-2x^4 - 7x^2 + x - 10)$

$gr = [2x^4 + 2x^3 + 5x^2 + 4x - x + 1 - 3 - (-2x^4 - 7x^2 + x - 10)] \\ \\ \\ gr = 2x^4 + 2x^3 + 8x^2 + 3-2- (-2x^4 - 7x^2 + x - 10) \\ \\ \\ => gr = 4x^4 + 2x^3 + 15x^2 + 2x + 8$

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b)
gr = [ P(x) -Q(x) - G(x)]

$gr = 2x^4 + 3x^2 + 4x + 1 - (2x^3 + 5x^2 - x - 3 ) - (-2x^4 - 7x^2 + x - 10) \\ \\ \\ gr = 2x^4 + 3x^2 + 4x + 1 + (2x^4 - 2x^3 + 2x^2 + 13 \\ \\ \\ => gr = 4x^4 - 2x^3 + 5x^2 + 4x + 14$