Question

Dado os polinômios: A=3X³-5X²+X-A, B=5X4-X³-X²+X-9 e C=X4 -16.

Determine:

A) A-B
B) A-C
C)A-B-C
D)Bxc

Answer 1

a)A-B=
(3x³-5x²+x-4) - (5x⁴-x³-x²+x-9) =
3x³-5x²+x-4-5x⁴+x³+x²-x+9=
5x⁴+3x³+x³-5x²+x²+x-x-4+9=
5x⁴+4x³-4x²+5

b) A-C=
(3x³-5x²+x-4)-(x⁴-16)
3x³-5x²+x-4-x⁴+16
x⁴+3x³-5x²+x-4+16
x⁴+3x³-5x²+x+12

c)A-B-C=
ja temos o valor de A-B lá na letra a, só subtrair C daquele resultado

(5x⁴+4x³-4x²+5)-(x⁴-16)
5x⁴+4x³-4x²+5-x⁴+16
5x⁴-x⁴+4x³-4x²+5+16
4x⁴+4x³-4x²+21

d) B*C
(5x⁴-x³-x²+x-9)*(x⁴-16) =
5x⁴*x⁴+5x⁴*(-16)-x³*x⁴-x³*(-16)-x²*x⁴-x²*(-16)+x*x⁴+x*(-16)-9*x⁴-9*(-16) =
5x^8-80x⁴-x^7+16x³-x^6+16x²+x^5-16x-9x⁴+144=
5x^8-x^7-x^6+x^5-80x⁴-9x⁴+16x³+16x²-16x+144=
5x^8-x^7-x^6+x^5-71x⁴+16x³+16x²-16x+144