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.
Discussion:
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.
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).
Discussion:
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).
Discussion:
⇒ 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)