Question

P(x)=x^3+3x^2+3x+1,g(x)=x+2

Answer 1

Step-by-step explanation:

p(x)= x^3+3x^2+3x+1

g(x)= x+2

divide both equation

we get

q(x) =x^2+x+1

Answer 2

$\huge{\underline{\tt{P(x)={x}^{3}+3x}^{2}+3x+1-}}}}$

$\huge{\underline{\tt{\green{Solution-}}}}$

$\longrightarrow \sf{g(x)=x-1}$

$\longrightarrow \sf{g(x)=0}$

$\longrightarrow \sf{x+1=0}$

$\longrightarrow \sf{x=-1}$

$\longrightarrow \sf{P(-1)=2{(-1)}^{3}+{x}^{2}-2x-1}$

$\longrightarrow \sf{P(-1)=2{(-1)}^{3}+{(-1)}^{2}-2\times-1-1}$

$\longrightarrow \sf{P(-1)=-2+1+2-1}$

$\longrightarrow \sf{P(-1)=0}$

$\longrightarrow \sf{x+1 is\:a\:factor\:of\:{2x}^{3}+{x}^{2}-2x-1}$