Question

Dados os polinômios:

f (x)= 2x³+3x=5
g(x)= x²-4x+2
h(x)= 2x³+5x-2

Calcule:

A) f (x)+g(x)=
B) f (x)+h(x)=
C) g(x)+h(x)=
D) f (x)-g(x)=
E) g(x)-h(x)=
F) f (x)-h(x)=
G) f (x)+g(x)-h(x)=
H)f(x).g(x)=
I) f(x).h(x)=
J) g(x).h(x)=

Answer 1

f (x)= 2x³+3x+5
g(x)= x²-4x+2
h(x)= 2x³+5x-2

Calcule:

A) f (x)+g(x)
= 2x³+3x+5 + x²-4x+2
= 2x³ + x² + 3x - 4x + 5 + 2
= 2x³ + x² -x + 7

B) f (x)+h(x)
= 2x³+3x+5 + 2x³+5x-2
= 2x³ + 2x³ + 3x + 5x + 5 - 2
= 4x³ = 8x + 3

C) g(x)+h(x)=
= x²-4x+2 + (2x³+5x-2)
= x² + 2x² - 4x + 5x + 2 - 2
= 3x² + x

D) f (x)-g(x)
= 2x³+3x+5 - (x²-4x+2)
= 2x³ + 3x + 5 - x² + 4x - 2
= 2x³ - x² + 3x + 4x + 5 - 2
= 2x³ - x² + 7x + 3

E) g(x)-h(x)=
= x²-4x+2 - (2x³+5x-2)
= x² - 4x + 2 - 2x² - 5x + 2
= -x² - 2x² -4x - 5x + 2 + 2
= -3x² - 9x + 4

F) f (x)-h(x)
= 2x³+3x+5 - (2x³+5x-2)
= 2x³ + 3x + 5 - 2x³ - 5x + 2
= 2x³ - 2x³ + 3x - 5x + 5 + 2
= -2x + 7

G) f (x)+g(x)-h(x)
=2x³+3x+5 +x²-4x+2 - (2x³+5x-2)
= 2x³ - 2x³ + x² + 3x - 4x - 5x + 5 + 2 + 2
= x² - 6x + 9

H)f(x).g(x)
=(2x³+3x+5).(x²-4x+2)
= 2x³.(x² - 4x + 2) + 3x.(x² - 4x + 2) + 5.(x² - 4x + 2)
= 2x⁵ - 8x⁴ + 4x³ + 3x³ - 12x² + 6 + 5x² - 20x + 10
= 2x⁵ - 8x⁴ + 7x³ - 7x² - 20x + 16

I) f(x).h(x)
= (2x³+3x+5).(2x³+5x-2)
= 2x³.(2x³ + 5x - 2) + 3x.(2x³ + 5x - 2) + 5.(2x³ + 5x - 2)
= 4x⁶ + 10x⁴ - 4x³ + 6x⁴ + 15x² - 6x + 10x³ + 25x - 10
= 4x⁶ + 16x⁴ + 6x³  + 15x² + 19x - 10

J) g(x).h(x)=
= (x²-4x+2).(2x³+5x-2)
= x².(2x² + 5x - 2) - 4x.(2x² + 5x - 2) + 2.(2x² + 5x - 2)
= 2x⁴ + 5x³ - 2x² - 8x³ - 20x² + 8x + 2x² + 10x - 4
= 2x⁴ + 5x³ - 8x³ - 2x² - 20x² + 2x² + 8x + 10x - 4
= 2x⁴ - 3x³ - 20x² + 18x - 4