Question

Fatore utilizando o teorema dos fatores:
$p(x) = 2 x^{3} + 3x {}^{2} + 2x - 2$
$p(x) = 3x {}^{3} - 4x {}^{2} - 7x - 2$
​

Answer 1

Resposta:

Para qualquer grau

P(x)=ax³+bx²+cx+d=a*(x-x')*(x-x'')*(x-x''')

A)

P(x)=2x³+3x²+2x-2

P(x)=2x³-x²+4x²+2x-2

P(x)=x²(2x-1)+4x²+2x-2

P(x)=x²(2x-1)+4x²+2x-2

####4x²+2x-2=0  

####x'=1/2 e x''=-1  ==>4x²+2x-2=4*(x+1)*(x-1/2)

P(x)=x²(2x-1)+4*(x+1)*(x-1/2)

P(x)=x²(2x-1)+2*(x+1)*(2x-1)

P(x)=x²(2x-1)+(2x+2)*(2x-1)

P(x)=(2x-1)*(x²+2x+2)

B)

P(x)=3x³-4x²-7x-2

P(x)=3x³+2x²-6x²-7x-2

P(x)=x²*(3x+2)-6x²-7x-2

####-6x²-7x-2=0

####x'=-2/3  e x''=-1/2  

####==>-6x²-7x-2=-6*(x+2/3)*(x+1/2)

P(x)=x²*(3x+2)-6*(x+2/3)*(x+1/2)

P(x)=x²*(3x+2)-2*(3x+2)*(x+1/2)

P(x)=x²*(3x+2)-(3x+2)*(2x+1)

P(x)=(3x+2)*(x²-2x-1)