__CHAPTER 2 POLYNOMIALS__

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DEGREE OF A POLYNOMIAL

The degree of a polynomial is the highest power of the variable. For e.g. in x^{3}+x^{2}+1 the degree is 2.

A polynomial of degree one is called a linear polynomial.

A polynomial of degree two is called a quadratic polynomial.

A polynomial of degree three is called is a cubic polynomial.

ZERO OF A POLYNOMIAL

A zero of a polynomial p(x) is a number c such that p(c)=0.

- A zero of a polynomial need not be 0.
- 0 may be a zero of a polynomial.
- Every linear polynomial has one and only one zero.
- A polynomial can have more than one zero.

REMAINDER THEOREM

Let p(x) be any polynomial of degree greater than or equal to one and let ‘a’ be any real number. If p(x) is divided by the linear polynomial x−a, then the remainder is p(a).

FACTOR THEOREM

If p(x) is a polynomial of degree n≥1 and is any real number, then:

- x−a is a factor of p(x), if p(a)=0, and
- p(a)=0, if x−a is a factor of p(x)

SOME MORE ALGEBRAIC 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-y)
^{3}= x^{3}-y^{3}-3xy(x-y) - x
^{3}+y^{3}+z^{3}-3xyz=(x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-zx)