Question

Dados lo polinomios:A(x)=3/5x^3-1/10x^2+x-3/2B(x)=5x^4+105x-7/2C(x)=2/5x^3-x-1Realiza los siguientes operacionesa.A(x)×B(x)b.A(x)×C(x)-x^2×B(x)c.[A(x)+B(x)]x+C(x)Por fa ayudenme!!!!urgente :(

Answer 1

A(x) = (3/5)x³ + (1/10)x² + x - 3/2

B(x) = 5x⁴ + 105x - 7/2

C(x) = (2/5)x³ - x - 1

a.

A(x) × B(x) =

[(3/5)x³ + (1/10)x² + x - 3/2] × [5x⁴ + 105x - 7/2] =

3x⁷ + (1/2)x⁶ + 5x⁵ + (63 - 15/2)x⁴ + (21/2 - 21/10)x³ + (105 - 7/20)x² - (315/2 - 7/2)x + 21/4

3x⁷ + (1/2)x⁶ + 5x⁵ + (111/2)x⁴ + (42/5)x³ + (2093/20)x² - 154x + 21/4

b.

A(x) × C(x) -x² × B(x)

[(3/5)x³ + (1/10)x² + x - 3/2] × [(2/5)x³ - x - 1] - x² × [5x⁴ + 105x - 7/2] =

(6/25)x⁶ + (1/25)x⁵ + (3/5 - 2/5)x⁴ - (3/5 + 3/5 + 1/10)x³ - (1 + 1/10)x² + (3/2 - 1)x + 3/2 - [5x⁶ + 105x³ - 7/2x²] =

(6/25)x⁶ + (1/25)x⁵ + (1/5)x⁴ - (13/10)x³ - (11/10)x² + (1/2)x + 3/2 - 5x⁶ - 105x³ + 7/2x² =

(1/25)x⁵ - (119/25)x⁶ + (1/5)x⁴ - (1063/10)x³ + (12/5)x² + (1/2)x + 3/2

c.

[A(x) + B(x)]x + C(x) =

[(3/5)x³ (1/10)x² + x - 3/2 + 5x⁴ + 105x - 7/2]x × [(2/5)x³ - x - 1] =

[5x⁴ + (3/5)x³ + (1/10)x² + 106x + 2]x × [(2/5)x³ - x - 1] =

[5x⁵ + (3/5)x⁴ + (1/10)x³ + 106x² + 2x] × [(2/5)x³ - x - 1] =

2x⁸ + (6/25)x⁷ - (5 - 1/25)x⁶ + (212/5 - 3/5 - 5)x⁵ + (4/5 - 1/10 - 3/5)x⁴ - (106 + 1/10)x³ - (106 + 2)x² - 2x =

2x⁸ + (6/25)x⁷ - (124/25)x⁶ + (184/5)x⁵ + (1/10)x⁴ - (1059/10)x³ - 108x² -2x