Question

Which of the following is a zero polynomial of x⁵-x³+2x-2 ​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{Polynomial\;is\;x^5-x^3+2x-2}$

$\underline{\textbf{To find:}}$

$\textsf{A zero of the given polynomial}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\:P(x)=x^5-x^3+2x-2}$

$\implies\mathsf{P(x)=x^3(x^2-1)+2(x-1)}$

$\implies\mathsf{P(x)=x^3(x^2-1^2)+2(x-1)}$

$\implies\mathsf{P(x)=x^3(x-1)(x+1)+2(x-1)}$

$\implies\mathsf{P(x)=(x^3(x+1)+2)(x-1)}$

$\implies\mathsf{P(x)=(x^4+x^3+2)(x-1)}$

$\mathsf{Now,}$

$\mathsf{P(1)=(1^4+1^3+2)(1-1)}$

$\mathsf{P(1)=0}$

$\therefore\mathsf{1\;is\;a\;zero\;of\;P(x)}$

$\underline{\textbf{Find more:}}$

Of one of the Zeroes of polynomial p (x)= (k-1) x²-kx +1 is ​

https://brainly.in/question/23339442

Answer 2

given,

x⁵-x³+2x-2

$=\left(x-1\right)\frac{x^5-x^3+2x-2}{x-1}\\=\left(x-1\right)\left(x^4+x^3+2\right)$