Polynomials meaning

Polynomials meaning

The Meaning Polynomial. In general, we can solve many tribal problems or polynomial with using the principle of the remaining theorem, the synthesis theorem, and the factor theorem principle. By master the three principles of the theorem, then many tribal issues will be resolved.

In addition to basic concepts, other things we must consider in solving a problem is to recognize the problem model. With lots of practice, then our treasury will be model-model the matter will grow and it will be very useful.

Begin to recognize the models that matter often appears. Here are some models of questions about the many tribes:

1. Determine the value of a large number of certain independent variables
2. Determine the many syllables if known only the divisor and the remaining division
3. Determine the quotient or the remaining division of a large tribe by a particular divisor
4. Determine the quotient or the remaining division of a large tribe by a divisor but a tribe much is unknown. The only known remains for many tribes if divided by some other dividers.
5. Determine the coefficient value of a large tribe if the remaining division and divisor are known.
6. Determining the roots of many tribes with factor theorems
7. Determine the factor of a large tribe

An example of a polynomial is x2 - 4 / x + 7x3/2 is not a polynomial.

Define polynomials

Polynomials/tribes are many forms of tribes with much finite arranged of variables and constants. The operation used is an only sum, education, multiplication and rank of non-negative integers.

Read Also : Degree of Polynomials Problems and Solving

In general, a polynomial can be written as follows.

Problem No.1

Arrange the 3x + x4 + 8 - 7x3 polynomials in the descending rank, then
a. state the tribes along with their coefficients,
b. state degree and constant.

Rearrange the 3x + x4 + 8 - 7x3 polynomial in the descending power cascade
the missing x variable. On the question, there is no term with the variable x2. Write the tribe as x4-7x3+ 0x2+ 3x + 8. The following is a polynomial in the descending rank order.

a. The polynomials and their coefficients are as follows.
tribe x4 coefficient 1
tribe -7x3 coefficient -7
trible 0x2 coefficient 0
tribe  3x coefficient 3
the term 8 is called a constant

b. The degree of the above polynomial is 4 since 4 is the highest rank of the variable. The lifting of the constant of the above polynomial is 8 since 8 is a non-existent term variable.

Problem No.2

Find the coefficient x3 and the constant of the polynomial 4x (x + 3) (x -2).


First, describe the polynomial into tribal forms.
4x (x + 3) (x -2) = 4x (x2 + 5x-6) = 4x3 + 20x2- 24x.

Of the  4x3 tribe, the coefficient  x3 obtained is 4. The constant of the above polynomial is 0.

Determining many tribal factors

According to the residual theorem, if a term of many f (x) is divisible by (x - a) or the remainder of the division is equal to zero, then (x - a) is called a multiplier factor f (x).
If in a term many f (x) apply f (a) = 0, f (b) = 0, and f (c) = 0, then (x - a), (x - b), and (x - c) are factors of many terms f (x) and f (x) will be divisible by them, while x = a, x = b, and x = c are the roots of the tribe many f (x) = 0.

If f (x) is divisible by (x - a) → f (a) = 0
If f (x) is divisible by (x + a) → f (-a) = 0
If f (x) is divisible by (ax - b) → f (b / a) = 0
If f (x) is divisible (ax + b) → f (-b / a) = 0

Problem No.1

Determine other factor of 2x3 - 4x2 - px + 1  is (x + 1).


⇒ f (x) = 2x3 - 4x2 - px + 1  of (x + 1) is obtained x = -1
⇒ f(-1) = 2(-1)3 - 4(-1)2 - p(-1) + 1
⇒ 0 = -2 - 4 + p + 1

⇒ 5 = p → substitution value p = 5 to many tribal functions
⇒ f (x) = 2x3 - 4x2 - 5x + 1
⇒ f (x) = (x+2)  (2x2 - 4x + 2)
 ⇒ f (x) = (x+2) (2x - 2) (x - 1)

so another factor is (2x - 2) and (x - 1)

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