Tag: introduction to unknowns

The given polynomial has three variables i.e.  $x, y$ and $z$ .

$\cfrac { { x^{ 3 }+2x+1 } }{ 5 } -\cfrac { 7 }{ 2 } x^ 2-x^ 6$
$=\cfrac { { x^{ 3 }+2x+1 } }{ 5 } -\cfrac { 7 }{ 2 } x^ 2-x^ 6$
$=-x^ 6+\cfrac { x^{ 3 } }{ 5 } -\cfrac { 7x^ 2 }{ 2 } +\cfrac { 2x }{ 5 } +\cfrac { 1 }{ 5 }$
So, the constant term= $\cfrac { 1 }{ 5 }$

A variable which can take real numbers only as its value is called as a real variable.

A polynomial in one variable must have non-negative integer exponents for the variable. Option A (x + 2/3 + 3) is a polynomial in x, whereas the others involve square roots of variables or multiple variables.

Given equation is $z^3+2z^2+5z+1$

$x^2+3x+5$
$=(2)^2+3\times 2+5$
$=4+6+5$
$=15$

$x^2+3x+5$
$=(-1)^2+3\times (-1)+5$
$=1-3+5$
$=6-3$
$=3$

$z^3+2z^2+5z+1$
$=(-1)^3+2\times (-1)^2+5\times (-1)+1$
$=-1+2-5+1$
$=-3$ 

$z^3+2z^2+5z+1$
$=(0)+2\times (0)^2+5\times (0)+1$
$=1$