Question

The division algorithm states that if​ p(x) and​ d(x) are polynomial functions with d left parenthesis x right parenthesis not equals 0 comma and the degree of​ d(x) is less than or equal to the degree of​ p(x), then there exist unique polynomial functions​ q(x) and​ r(x) such that

Answer 1

Answer:

I guess you ran out of space

Step-by-step explanation:

I think you have to prove that you get a line. Just take the limit of the resulting remainder. That goes to zero.

Answer 2

Answer:

In a division algorithm, $p(x)$ refers to the dividend polynomial, $d(x)$ refers to the divisor polynomial, $q(x)$ refers to the quotient polynomial and $r(x)$ refers to the residula polynomial.

The division algorithm is defined as

$p(x)=d(x) \times q(x) +r(x)$

Where $p(x)\geq d(x)$ and $d(x) \neq 0$, other wise the algorithm won't be defined.

So, the complete paragraph is: "if $p(x)$ and $d(x)$ are polynomial functions with $d(x)\neq 0$ and the degree of $d(x)$ is less than or equal to the degree of $p(x)$, then there exist unique polynomial functions $q(x)$ and $r(x)$ such that  $p(x)=d(x) \times q(x) +r(x)$.