Question

considere os polinômios
A= x² + 2x, B = 3x - 1 e C = 2x² -2x + 1
a) A - B
b) A . B
c) A - C . B
d) B . (A - C)

Answer 1

a)

(x²+2x)-(3x-1) = x²+2x-3x+1 = x²-x+1

b)

(x²+2x)(3x-1) = x²(3x)+x²(-1)+2x(3x)+2x(-1) = 3x³-x²+6x²-2x
(x²+2x)(3x-1) = 3x³+5x²-2x

c)

(x²+2x)-(3x-1)(2x²-2x+1) = (x²+2x)-(6x³-8x²+5x-1) = -6x³+9x²-3x+1

(3x-1)(2x²-2x+1) = 3x(2x²)+3x(-2x)+3x(1)-1(2x²)-1(-2x)-1(1)
(3x-1)(2x²-2x+1) = 6x³-6x²+3x-2x²+2x-1 = 6x³-8x²+5x-1

(x²+2x)-(6x³-8x²+5x-1) = x²+2x-6x³+8x²-5x+1 = -6x³+9x²-3x+1

d)

(3x-1)(x²+2x-(2x²-2x+1)) = (3x-1)(-x²+4x-1) = -3x³+12x²-3x+x²-4x+1
(3x-1)(x²+2x-(2x²-2x+1)) = -3x³+13x²-7x+1

(x²+2x-(2x²-2x+1)) = x²+2x-2x²+2x-1 = -x²+4x-1

(3x-1)(-x²+4x-1) = 3x(-x²)+3x(4x)+3x(-1)-1(-x²)-1(4x)-1(-1)
(3x-1)(-x²+4x-1) = -3x³+12x²-3x+x²-4x+1 = -3x³+13x²-7x+1