A simplified method of "signal and system" polynomial

1. Polynomial Long Division

Brief introduction???

? ? ? Polynomial long division? is an algorithm in algebra that removes another polynomial by using a polynomial of the same or lower number of times. is a generalized version of the common arithmetic technique of long division. It can be easily hand-counted because it breaks down a relatively complex division problem into smaller problems.

Example

Calculation

?

1. The removal of the type, in addition to a letter to the power of descending order, and the missing items with 0, written in the following form:

?

1. The quotient and remainder can then be calculated as follows:

Divides the first item of the numerator by the highest occurrence of the denominator (that is, the highest number of items, here is x). The result is written on the horizontal line (X3?÷?X?=?X2).

1. Multiply the denominator by just getting the result (the first item of the final quotient), and the product is written under the first two elements of the molecule (similar terms) (x2?? (X??? 3) =?x3??? 3x2).

1. Subtract the newly obtained product from the corresponding term of the molecule (eliminate the equal items, combine the unequal items), and the result is written below. (X3??? 12X2)??? (X3??? 3x2) = 12x2?+?3x2?=? 9x2) Then, "Take down" the next item of the molecule.

1. The difference is treated as a new de-duplication, repeating the first three steps (until the number of zeros or the remainder of the formula is less than the number of times the formula is removed). (except type x quotient + redundancy)

1. Repeat the fourth step. Nothing can be "taken down" this time.

1. The polynomial above the line is the quotient, and the remaining (123) is the remainder.

?

?

?

Division transformation

Using a polynomial long division can write a polynomial in the form of a divisor-quotient (often useful). Consider the polynomial? P (x),? Number of D (x) ((d) < (P)). And then, to a certain quotient polynomial? Q (x) and remainder polynomial R (x) (coefficients of (R) < (D),

This transformation is called the Division transformation, is it from the arithmetic equation? [1]? Get the.

?

Original address: http://zh.wikipedia.org/wiki/%E5%A4%9A%E9%A1%B9%E5%BC%8F%E9%95%BF%E9%99%A4%E6%B3%95

?

1. Partial Fractional expansion method

When the denominator is a single-item of a higher power.

We can first set the coefficients of the power from low to high order, as shown in.

? After the fraction is removed from the denominator, the equations of coefficients a, B, and C are listed according to the principle of the polynomial which is equal to the two polynomial.

?

To solve the equations, the values of A, B and C are obtained, and the polynomial with coefficients is then listed.

?

So when the denominator is a single-item of multiple powers, we can list each individual as a denominator, and then set the numerator to the selected factor.

?

After the denominator is removed, the value of the coefficients a, B, and C is solved by false attempts to assume the value of x based on the individual formula in the denominator (that is, the value of single-item equals zero).

?

The final result can be obtained by substituting the coefficients obtained.

?

You can also use synthetic division, as follows:

Some excerpts from the network

A simplified method of "signal and system" polynomial