Why degree of remainder is less than degree of divisor

In this video we discuss about why the remainder always smaller than the divisor, it is quite obvious when we deal with numbers but less difficult to see when we deal with algebra unknowns.

Here, the case we are dealing with is with polynomials.
we Let f(x) be the dividend
Q(x) be the quotient
R(x) be the remainder
D(x) be the divisor
We look at the case when the degree of D(x) is equal to the degree of f(x) and then the degree of D(x) is less than the degree of f(x) and show that for both cases, the degree of R(x) is less than the degree of D(x).

We excluded the case where the degree of D(x) is 0 meaning it is a constant as the remainder would be 0.

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