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

I guess you ran out of space

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

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) * q(x) +r(x)`

Where
`p(x)\geq d(x)` and
`d(x) \\eq 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)\\eq 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) * q(x) +r(x)`.