POLYNOMIALS - NCERT

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IntroductionYou have studied algebraic expressions, their addition, subtraction, multiplication anddivision in earlier classes. You also have studied how to factorise some algebraicexpressions. You may recall the algebraic identities :(x + y)2 =x2 + 2xy + y2(x y)2 =x2 2xy + y2andx2 y2 =(x + y) (x y)and their use in factorisation. In this chapter, we shall start our study with a particulartype of algebraic expression, called polynomial, and the terminology related to it. Weshall also study the Remainder Theorem and Factor Theorem and their use in thefactorisation of POLYNOMIALS . In addition to the above, we shall study some more algebraicidentities and their use in factorisation and in evaluating some given POLYNOMIALS in One VariableLet us begin by recalling that a variable is denoted by a symbol that can take any realvalue.

POLYNOMIALS 31 Now observe the polynomials p(x) = 4x + 5, q(y) = 2y, r(t) = t + 2 and s(u) = 3 – u.Do you see anything common among all of them? The degree of each of these polynomials is one. A polynomial of degree one is called a linear polynomial. Some more linear polynomials in one variable are 2 x – 1, 2 y + 1, 2 – u.Now , try and

  Polynomials