Question

me piden ayudar a resolver, no le entiendo.


Dados los polinomios A(x) = 3x4 + 5x³ − 2x² + x − 7, B(x) = 8x³ − 6x² − 3, C(x) = 4x5 + 9x4 + 5, D(x) = 6x² − x7 − 6x5 + 4x, realiza las operaciones que se indican a continuación:

• A(x) + B(x) = ()x4 + ( )x3 - (2)x2 + ( )x – ( )
• A(x) - B(x) = ( )x4 - ( )x3 + ( )x2 + ( )x – ( )
• 3A(x) − B(x) − C(x) = - ( )x5 + ( )x4 + ( )x3 + ( )x2 + ( )x – ( )
• 2A(x) − 4B(x) + 8D(x) = = - ( )x7 + ( )x6 - ( )x5 + ( )x4 - ( )x3 + ( )x2 + ( )x – ( )

Answer 1

Respuesta:

A(x) + B(x) =

$3{x}^{4} + 13{x}^{3} - 8{x}^{2} + x - 10$

A(x) - B(x) =

$3{x}^{4} - 3{x}^{3} + 4{x}^{2} + x - 4$

3A(x) - B(x) - C(x) =

$-4 {x}^{5} + 7{x}^{3} + 3x - 23$

2A(x) - 4B(x) + 8D(x) =

$- \: 8 {x}^{7} - 48 {x}^{5} + 6 {x}^{4} - 22 {x}^{3} + 68{x}^{2} + 34x - 2$

Explicación paso a paso:

Los polinomios son:

$a(x) = 3{x}^{4} + 5{x}^{3} - 2 {x}^{2} + x - 7 \\ b(x) = 8 {x}^{3} - 6 {x}^{2} - 3 \\ c(x) = 4 {x}^{5} + 9 {x}^{4} + 5 \\ d(x) = 6 {x}^{2} - {x}^{7} - 6 {x}^{5} + 4x$

Operaciones:

A(x) + B(x) =

$3{x}^{4} + 5{x}^{3} - 2 {x}^{2} + x - 7 + (8 {x}^{3} - 6 {x}^{2} - 3)$

A(x) - B(x) =

$3{x}^{4} + 5{x}^{3} - 2 {x}^{2} + x - 7 - (8 {x}^{3} - 6 {x}^{2} - 3)$

3A(x) - B(x) - C(x) =

$3 \times (3{x}^{4} + 5{x}^{3} - 2 {x}^{2} + x - 7) - (8 {x}^{3} - 6 {x}^{2} - 3) - (4 {x}^{5} + 9 {x}^{4} + 5)$

2A(x) - 4B(x) + 8D(x)

$2 \times (3{x}^{4} + 5{x}^{3} - 2 {x}^{2} + x - 7) - 4 \times (8 {x}^{3} - 6 {x}^{2} - 3) + 8 \times (6 {x}^{2} - {x}^{7} - 6 {x}^{5} + 4x)$