Write the necessary and sufficient condition for the polynomial
$p (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . + a_{n}$
to be a polynomial of order $(n - 2)$ .

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Solution

Given that,
$p (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} . . . . . . . . a_{n}$
It will be polynomial of order $(n - 2)$
If coefficient of higher order be $Z e r o$
and $n - 2 \in$ Integers.
i.e: $a_{0} = a_{1} = 0 a n d n - 2 \in I$

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Write the necessary and sufficient condition for the polynomial p(x)=a0xn+a1xn−1+a2xn−2+...+an to be a polynomial of order (n−2).

Given that,p(x)=a0xn+a1xn−1+a2xn−2........anIt will be polynomial of order (n−2)If coefficient of higher order be Zeroand n−2∈ Integers.i.e:a0=a1=0andn−2∈I

Write the necessary and sufficient condition for the polynomial
$p (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . + a_{n}$
to be a polynomial of order $(n - 2)$ .

Given that,
$p (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} . . . . . . . . a_{n}$
It will be polynomial of order $(n - 2)$
If coefficient of higher order be $Z e r o$
and $n - 2 \in$ Integers.
i.e: $a_{0} = a_{1} = 0 a n d n - 2 \in I$