Question

Considere os seguintes polinômios:

P = 3x² + 5x - 1
Q = x³ + 8² - 5x + 1
R = 6 - x³ - 3x²

A) P + Q
B) P - Q
C) P + Q + R
D) Q - P + R

Answer 1

A)_ Resolução:

(3x² + 5x - 1) + (x³ + 8² - 5x + 1)
x³ + 3x² + 5x - 5x - 1 + 1 + 64
x³ + 3x² + 64

B)_ Resolução:

(3x² + 5x - 1) - (x³ + 8² - 5x + 1)
3x² + 5x - 1 - x³ - 64 + 5x - 1
-x³ + 3x² + 10x - 66

C)_ Resolução:

(3x² + 5x - 1) + (x³ + 8² - 5x + 1) + (6 - x³ - 3x²)
x³ + 3x² + 5x - 5x - 1 + 1 + 64 + (6 - x³ - 3x²)
x³ + 3x² + 64 + 6 - x³ - 3x²
x³ - x³ + 3x² - 3x² + 64 + 6
70

D)_ Resolução:

(x³ + 8² - 5x + 1) - (3x² + 5x - 1) + (6 - x³ - 3x²)
x³ - 3x² - 10x + 64 + 2 + (6 - x³ - 3x²)
x³ - 3x² - 10x + 66 + 6 - x³ - 3x²
x³ - x³ - 3x² - 3x² - 10x + 72
-6x² - 10x + 72

Espero ter ajudado!

Answer 2

Oie, Td Bom?!

• Sabendo que:

$P = 3x {}^{2} + 5x - 1$

$Q= x {}^{3} + 8 {}^{2} - 5x + 1$

$R= 6 - x {}^{3} - 3x {}^{2}$

A)

$= P + Q$

$= (3x {}^{2} + 5x - 1) + (x {}^{3} + 8 {}^{2} - 5x + 1)$

$= 3x {}^{2} + 5x - 1 + (x {}^{3} + 64 - 5x + 1)$

$= 3x {}^{2} + 5x - 1 + (x {}^{3} + 65 - 5x)$

$=3x {}^{2} + 5x - 1 + x {}^{3} + 65 - 5x$

$= 3x {}^{2} + 64 + x {}^{3}$

$= x {}^{3} + 3x {}^{2} + 64$

B)

$= P - Q$

$= (3x {}^{2} + 5x - 1) - (x {}^{3} + 8 {}^{2} - 5x + 1)$

$= 3x {}^{2} + 5x - 1 - (x {}^{3} + 64 - 5x + 1)$

$= 3x {}^{2} + 5x - 1 - (x {}^{3} + 65 - 5x)$

$= 3x {}^{2} + 5x - 1 - x {}^{3} - 65 + 5x$

$= 3x {}^{2} + 10x - 66 - x {}^{3}$

$= - x {}^{3} + 3x {}^{2} + 10x - 66$

C)

$=P+ Q + R$

$= (3x {}^{2} + 5x - 1) + (x {}^{3} + 8 {}^{2} - 5x + 1) + (6 - x {}^{3} - 3x {}^{2} )$

$= 3x {}^{2} + 5x - 1 + (x {}^{3} + 64 - 5x + 1) + 6 - x {}^{3} - 3x {}^{2}$

$= 3x {}^{2} + 5x - 1 + (x {}^{3} + 65 - 5x) + 6 - x {}^{3} - 3x {}^{2}$

$= 3x {}^{2} + 5x - 1 + x {}^{3} + 65 - 5x + 6 - x {}^{3} - 3x {}^{2}$

$= 3x {}^{2} - 1 + x {}^{3} + 65 + 6 - x {}^{3} - 3x {}^{2}$

$= - 1 + x {}^{3} + 65 + 6 - x {}^{3}$

$= - 1 + 65 + 6$

$= - 1 + 71$

$= 70$

D)

$= Q - P + R$

$= (x {}^{3} + 8 {}^{2} - 5x + 1) - (3x {}^{2} + 5x - 1) + (6 - x {}^{3} - 3x {}^{2} )$

$= (x {}^{3} + 64 - 5x + 1) -( 3x {}^{2} + 5x - 1) + 6 - x {}^{3} - 3x {}^{2}$

$= (x {}^{3} + 65 - 5x) - (3x {}^{2} + 5x - 1) + 6 - x {}^{3} - 3x {}^{2}$

$= x {}^{3} + 65 - 5x - (3x {}^{2} + 5x - 1) + 6 - x {}^{3} - 3x {}^{2}$

$= 65 - 5x - 3x {}^{2} - 5x + 1 + 6 - 3x {}^{2}$

$= 72 - 5x - 3x {}^{2} - 5x - 3x {}^{2}$

$= 72 - 10x - 3x {}^{2} - 3x {}^{2}$

$= 72 -10x - 6x {}^{2}$

$= - 6x {}^{2} - 10x + 72$

Att. Makaveli1996