02. Polynomials

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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 ax2 + 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  = x2 + y2 + z2 + 2xy + 2yz + 2zx

(x ± y)3  = x3 ± y3 ± 3xy (x ± y)

x3 ± y3   = (x ± y) (x2 ± xy + y2)

x3 + y3 + z3 -3xyz   = (x + y + z) (x2 + y2 + z- xy – yz - zx)

and their use in

factorization of polynomials.