Question

Considerando los siguientes polinomios:

A(x) = 3x² - 5x + 2

B(x) = 4x³+ 3x² + 2x - 5

C(x) = -4x + x³ + 3

D(x) = 2x⁴ + 5x² - 7

Calcular:

a. B(x) + C(x)

b. A(x) + D(x)

c. B(x) + D(x)

d. A(x) + C(x)

e. A(x) + B(x) + C(x)

Ayuda por fis

Answer 1

Respuesta:

$a) B (x) + C (x) = (4 {x}^{3} + 3 {x}^{2} + 2x - 5 ) + ( - 4x + {x}^{3} + 3) = 4 {x}^{3} + 3 {x}^{2} + 2x - 5 - 4x + {x}^{3} + 3 = 5 {x}^{3} + 3 {x}^{2} - 2x - 2$

$b) A(x) + D (x) = (3 {x}^{2} - 5x + 2 ) + (2 {x}^{4} + 5 {x}^{2} - 7 ) = 3 {x}^{2} - 5x + 2 + 2 {x}^{4} + 5 {x}^{2} - 7 =2 {x}^{4} + 8 {x}^{2} - 5x - 5$

$c) B(x ) + D (x) = (4 {x}^{3} + 3 {x}^{2} + 2x - 5 ) + (2 {x}^{4} + 5 {x}^{2} - 7 ) = 4 {x}^{3} + 3 {x}^{2} + 2x - 5 + 2 {x}^{4} + 5 {x}^{2} - 7 = 2 {x}^{4} + 4 {x}^{3} + 8 {x}^{2} + 2x - 12$

$d)A(x) + C (x) = (3 {x}^{2} - 5x + 2) + ( - 4x + {x}^{3} + 3 ) = 3 {x}^{2} - 5x + 2 - 4x + {x}^{3} + 3 = {x}^{3} + 3 {x}^{2} - 9x + 5$

$e) A(x) + B(x + )C (x) = (3 {x }^{2} - 5x + 2) + (4 {x}^{3} + 3 {x}^{2} + 2x - 5 ) + ( - 4x + {x}^{3} + 3 ) = 3 {x}^{2} - 5x + 2 + 4 {x}^{3} + 3 {x}^{2} + 2x - 5 - 4x + {x}^{3} + 3 = 5 {x}^{3} + 6 {x}^{2} - 7x$