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இயற்கணித வெளிப்பாடு என்ற தலைப்பின் கீழ் முந்தைய வகுப்பில் கற்ற சொற்களை நினைவு கூர்வோம் ::
மாறிகள்:ஒரு மாறி என்பது அறியப்படாத மதிப்பு குறியீடு. இது பொதுவாக இவ்வாறு குறிக்கப்படுகிறது\(x\), \(y\), \(a\), \(b\).
மாறிலி: எந்த மாறியும் இல்லாமல் தனித்து நிற்கும் ஒரு எண் மாறிலி எனப்படும்.
உறுப்புகள்: உறுப்புகள் என்பது மாறிகள், எண்கள் அல்லது மாறிகள் எண்களால் பெருக்கப்படும் கோவை. கூட்டல் மற்றும் கழித்தல் போன்ற இயற்கணிதச் செயல்பாடு விதிமுறைகளைப் பிரிக்கிறது.
கெழு: A coefficient can either be a numerical factor or an algebraic factor or product of both that is a number used to multiply a variable.
Polynomial is a type of algebraic expression.
Let us see the concept of the polynomial.
Polynomial is an expression consisting of variables and coefficients which involves operations such as addition, subtraction, multiplication, and non-negative integer exponents.
Consider an expression  p(x)=x2 − 8x + 9.
The above expression is a polynomial expression because the expression involves the variables(\(x\)) and coefficients, and the terms are separated by subtraction and addition. Also, the exponents(\(x^{2}\) and \(x\)) of the variables are non-negative integers.
Where \(p(x)\) is the polynomial of \(x\), \(x\) is the variable, \(1\) is the coefficient of \(x²\), \(-8\) is the coefficient of \(x\), and \(9\) is the constant.
Polynomials are generally indicated based on the variables involved in the expression. If the variable in the polynomial is '\(x\)', then it can be denoted as p(x) or q(x) or r(x), etc.
Let us check the following algebraic expressions are polynomials or not.
1. \(x^{2} + 6x\)
Here the terms \(x^{2}\) and \(6x\) are connected by addition operation, and exponents of the variable \(x\) is a whole number.
Thus, the expression \(x^{2} + 6x\) is a polynomial expression.
2. \(\frac{1}{x}\).
The reciprocal of the expression is \(x^{-1}\).
Thus, the expression has a negative exponent.
Therefore, the expression is not a polynomial.
3. \(y^{3}-3x^{2}y+3xy^{2}+x^{3}\)
Here the terms \(y^{3}\), \(3x^{2}y\), \(3xy^{2}\) and \(x^{3}\) are connected by addition and subtraction.
Also, the exponents of all the variables(powers of \(x\) and \(y\)) are the whole number.
Thus, the expression \(y^{3}-3x^{2}y+3xy^{2}+x^{3}\) is a polynomial expression.
4. \(z^{3}-8\sqrt{z}\)
The exponent of \(z\) in the second term is \(\frac{1}{2}\). It is not a whole number.
Thus, the expression has non-integer exponent.
Therefore, the expression is not a polynomial.
Polynomials in day-to-day life:
1. Polynomials are typically used in the fields of Physics, Chemistry, Civil Engineering, Finance, and so on.
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2. A polynomial can be graphically represented.
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