# 02. Polynomials

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#### Description:

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials;monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of *ax _{2 }+ bx + c*, a → 0 where a b and c are real numbers, and of cubic polynomials using the FactorTheorem.

Recall of algebraic expressions and identities. verification of identities:

*(x+y+z) ^{2 }= x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2zx*

*(x ± y) ^{3 }= x^{3} ± y^{3} ± 3xy (x ± y)*

*x ^{3} ± y^{3} ^{ }= (x ± y) (x^{2} ± xy + y^{2})*

*x ^{3} + y^{3 }+ z^{3 }-3xyz ^{ }= (x + y + z) (x^{2} + y^{2} + z^{2 }- xy – yz - zx)*

and their use in

factorization of polynomials.