Question

if x+1 is a factor of ax4+bx3+cx2+dx+e show that a+c+e=b+d ​

Answer 1

Answer:

See explanation

Step-by-step explanation:

Concept : If $x-a$ is a factor of a polynomial P(x), then $P(a)=0$

Here given $x+1=x-(-1)$ is a factor of $P(x)=ax^4+bx^3+cx^2+dx+e$

        $\Rightarrow P(-1)=0\\\Rightarrow a(-1)^4+b(-1)^3+c(-1)^2+d(-1)+e=0\\\Rightarrow a-b+c-d+e=0\\\Rightarrow a+c+e=b+b$

Hence proved