Question

Dados os polinômios P1 (x) = x^3 + 1, P2 (x) = x + 1 e P3 (x)= ax^2 + bx + c, determine a, b e c, para que P1 (x)= P2 (x). P3(x)

Answer 1

 

 P1 (x) = x^3 + 1, P2 (x) = x + 1 e P3 (x)= ax^2 + bx + c

 

 P1 (x)= P2 (x). P3(x)

 

x^3 + 0x^2 + 0x + 1 = ( x + 1)( ax^2 + bx + c)

 

x^3 + 0x^2 + 0x + 1 = ax^3 + bx^2 + cx + ax^2 + bx + c

 

1 = a 

0 = a + b  => b = - a ==> b = - 1

0 = c + b

1 = c

Answer 2

Resposta:

P1 (x) = P2 (x) . P3(x)

X³ + 0x² + 0x + 1 = ( x + 1)( ax² + bx + c)

X³ + 0x² + 0x + 1 = ax³ + bx² + cx + ax² + bx+c

1=a

0 = a + b => b= -a ==> b=-1

0 = c + b

1 = c