The word ‘poly’ that is often used in math is actually derived from Greek. ‘Poly’ in that language means ‘many’. So, if an expression has many terms, then it is called as polynomial. But the number of terms has to be finite. Generally up to three terms expressions have their own identities like a single term is called a monomial, two terms as binomial and three terms as trinomial. Polynomials (abbreviated as Pnml) can also form the core part of a function, in such cases they are called as polynomial functions.
From what we described any expression or any function which has many terms could be Pnmls. Is this statement correct? No, there is a limitation. Only expressions in which no term is divided by any variable and do not contain a non-negative exponent terms can be referred as Pnmls.
In this topic of polynomials help, we will see some examples of polynomials and how to simplify polynomials.The following are the polynomials examples.
2x^3 + 3x^2 – 7x + 2
6x4 – 2x^3 + 4x^2 + 2x + 9
4x^3y^2 – x^2y^2 + 2xy - 14
5x^3 + (x^2/2) + 4x –7
In the third example we find three terms contain two variables but it does not matter as far as the definition of Pnml is concerned.
In the last example one can notice that one of the terms (the second term) is divided by 2. But it does not affect the Pnml status of the expression as 2 is only a constant. Only when any term is divided by any variable cannot qualify to be a Pnml.
The following expressions cannot be called as Pnmls.
x^3 + 4x^2 – 7x + (2/x)
6x4 – 2x-3 + 4x^2 + 2x + 9
7x^3– 2x^2 + 5x^2/3 + x + 1
1 + (x/1!) + (x^2/2!) + (x^3/3!) + …….
In the first expression, the last term is divided by a variable. In the second expression we find a negative exponent in the second term. The third term of the the third expression has a rational exponent which cannot be simplified as an integer. The fourth expression has infinite number of terms. Hence all of them cannot qualify as Pnmls.
It is possible that a Pnml may have exactly similar terms excepting that the coefficients may be different. Those terms are called like terms. Such expressions can be simplified by algebraically adding the like terms. Similarly a Pnml can be simplified and expressed in factored form by identifying common factors. Simplified Pnmls show a better presentation.
From what we described any expression or any function which has many terms could be Pnmls. Is this statement correct? No, there is a limitation. Only expressions in which no term is divided by any variable and do not contain a non-negative exponent terms can be referred as Pnmls.
In this topic of polynomials help, we will see some examples of polynomials and how to simplify polynomials.The following are the polynomials examples.
2x^3 + 3x^2 – 7x + 2
6x4 – 2x^3 + 4x^2 + 2x + 9
4x^3y^2 – x^2y^2 + 2xy - 14
5x^3 + (x^2/2) + 4x –7
In the third example we find three terms contain two variables but it does not matter as far as the definition of Pnml is concerned.
In the last example one can notice that one of the terms (the second term) is divided by 2. But it does not affect the Pnml status of the expression as 2 is only a constant. Only when any term is divided by any variable cannot qualify to be a Pnml.
The following expressions cannot be called as Pnmls.
x^3 + 4x^2 – 7x + (2/x)
6x4 – 2x-3 + 4x^2 + 2x + 9
7x^3– 2x^2 + 5x^2/3 + x + 1
1 + (x/1!) + (x^2/2!) + (x^3/3!) + …….
In the first expression, the last term is divided by a variable. In the second expression we find a negative exponent in the second term. The third term of the the third expression has a rational exponent which cannot be simplified as an integer. The fourth expression has infinite number of terms. Hence all of them cannot qualify as Pnmls.
It is possible that a Pnml may have exactly similar terms excepting that the coefficients may be different. Those terms are called like terms. Such expressions can be simplified by algebraically adding the like terms. Similarly a Pnml can be simplified and expressed in factored form by identifying common factors. Simplified Pnmls show a better presentation.
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