# Definition of Polynomials

polynomials in x degree n are a form

a

_{n}x^{n}+ a_{n-1 }x^{n-1}+ a_{n-2 }x^{n-2}+ … + + a_{2 }x^{2}+ a_{1}x + a_{0}
for n a chunk number, and a

_{0}, a_{1}, …, a_{n }as a constant and a_{n}≠ 0.
In a polynomial where a

_{1}, …, a_{n}is called the tribal coefficient x. The number n is called the polynomial quality. The form of writing a polynomial is arranged with the highest rank base placed in the front row, while the smaller rank is on the right. An example is writing the following polynomial 4.
2x

^{4}– 7x^{3}+ 5x – 9
Description: The coefficient of x

^{4 }is 2, the coefficient of x^{3}is -7, the coefficient of x is 5, the constant is -9.### Polynomial Value

To facilitate the method of mentioning polynomials it is often expressed by the form function f(x). To determine the value of a polynomial is to replace x with a constant.

Example 1.

Determine the value of the polynomial, 4x

^{4}– 3x + 6 for x = 2
Answer:

f(x) = 4x

^{4}– 3x + 6
substitute the value x = 2 to f(x)

f(2) = 4 . 2

^{4}– 3 . 2 + 6 = 64 – 6 + 6 = 64
Such a method is indeed quite simple, but for polynomials with a high enough taste or a relatively high number of tribes, then this method can obviously cause difficulties in the calculation. For this reason, consider a more systematic way to calculate polynomial values as follows,

For example to obtain a polynomial value, consider the following polynomial,

2x

^{3}+ 4x^{2}– 3x + 2We can express the polynomial with the following form of writing

f(x) = 2x

^{3}+ 4x^{2}– 3x + 2
f(x) = (2x

^{2}+ 4x – 3)x + 2
f(x) = [(2x + 4)x – 3]x + 2

by using the form of writing above, the polynomial value for x = 5 is

f(x) = [(2x + 4)x – 3]x + 2

f(5) = [(2 . 5 + 4)5 – 3]5 + 2

f(5) = [(10 + 4)5 – 3]5 + 2

f(5) = [14 . 5 + (– 3)]5 + 2

f(5) = [70 + (– 3)]5 + 2

f(5) = 67 . 5 + 2 = 335 + 2 = 337

The pattern seen in the above calculation is as follows,

Multiply (dot ".") 2 by 5, then add 4 then get 14.

Multiply 14 by 5, then add -3 then get 67.

Multiply 67 by 5, then add 2, then get 337.

The process can be presented with a more interesting scheme below,

Description: arrow indicates multiplied by 5

Example 2.

Calculate f (-2) for f(x) = 3x

^{3}– 4x + 6.
Answer:

Using the schematic that has been studied above, arrange the numbers in the first row that contain each x coefficient from the highest rank down to the lower rank.

So, f(-2) = - 10

Description: because the coefficient of x

^{2}does not exist, then where the coefficient in question is written zero.SUBSCRIBE TO OUR NEWSLETTER

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