4.3 Polynomial Division and Synthetic Division

In the long division process for polynomials, we divide the dividend P(x) by the divisor D(x)≠0 to obtain a quotient Q(x) and a remainder R(x) then we have P(x)/D(x) = Q(x)+R(x)/D(x)

where R(x)=0 or where degree of R(x)< degree of D(x) which can also be written as P(x)=Q(x)D(x)+R(x) (called the division algorithm - which a good tool to check your equations)

*4.3C Polynomial Division When The Divisor is not x-r/Quadratic Divisor*

(Brian McLogan) https://www.youtube.com/watch?v=SbUiZx5a0Ok

*4.3a Polynomial Division*

(NancyPi) https://www.youtube.com/watch?v=RPXMBIFG_W4

*4.3D and Example 2: Synthetic Division*

(Nancypi) https://www.youtube.com/watch?v=AWCQBLthbNI

Thus we can write: p/d = q + r/d where, 0≤r<d...This result can also be written in the form p=qd+r

For example: 7284/13 = 560+4/13 (or) 7284=(560)(13)+4

To find the zeros of a polynomial, its necessary to divide the polynomial by a second polynomial. There is a procedure for polynomial division that parallels the long division process of arithmetic.

In arithmetic, if we divide an integer p by an integer d≠0, we obtain a quotient q and a remainder r