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Danwinster10
@Danwinster10
January 2020
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Seja o polinômio P (x)= x ao cubo + 3x ao quadrado - 2x + 1 o valor de P(0) + P(-1) + P(1) + P(-2) é
A 16
B 17
C 18
D 19
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Rodrigo3200
Dado:
P(x) = x³ + 3x² - 2x + 1 (1)
Substitua na equação (1)
x por 0
P(0) = 0³ + 3.0² - 2.0 + 1
P(0) = 0 + 3.0 - 0 + 1
P(0) = 0 + 0 - 0 + 1
P(0) = 1
x por (-1)
P(-1) = (-1)³ + 3.(-1)² - 2.(-1) + 1
P(-1) = -1 + 3.1 + 2 + 1
P(-1) = -1 + 3 + 2 + 1
P(-1) = 5
x por 1
P(1) = 1³ + 3.1² - 2.1 + 1
P(1) = 1 + 3.1 - 2 + 1
P(1) = 1 + 3 - 2 + 1
P(1) = 3
x por (-2)
P(-2) = (-2)³ + 3.(-2)² - 2.(-2) + 1
P(-2) = -8 + 3.4 + 4 + 1
P(-2) = -8 + 12 + 4 + 1
P(-2) = 9
Portanto:
P(0) + P(-1) + P(1) + P(-2) = 1 + 5 + 3 + 9 = 18
(C)
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Danwinster10
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P(x) = x³ + 3x² - 2x + 1 (1)
Substitua na equação (1)
x por 0
P(0) = 0³ + 3.0² - 2.0 + 1
P(0) = 0 + 3.0 - 0 + 1
P(0) = 0 + 0 - 0 + 1
P(0) = 1
x por (-1)
P(-1) = (-1)³ + 3.(-1)² - 2.(-1) + 1
P(-1) = -1 + 3.1 + 2 + 1
P(-1) = -1 + 3 + 2 + 1
P(-1) = 5
x por 1
P(1) = 1³ + 3.1² - 2.1 + 1
P(1) = 1 + 3.1 - 2 + 1
P(1) = 1 + 3 - 2 + 1
P(1) = 3
x por (-2)
P(-2) = (-2)³ + 3.(-2)² - 2.(-2) + 1
P(-2) = -8 + 3.4 + 4 + 1
P(-2) = -8 + 12 + 4 + 1
P(-2) = 9
Portanto:
P(0) + P(-1) + P(1) + P(-2) = 1 + 5 + 3 + 9 = 18 (C)