DONE BY: R.PRINCE

POLYNOMIALSIn mathematics,

a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

EXAMPLEAn example of a polynomial of a

single indeterminate (or variable), x, is x2 − 4x + 7, which is a quadratic polynomial.

HISTORYDetermining the roots of

polynomials, or "solving algebraic equations", is among the oldest problems in mathematics.

The elegant and practical notation we use today only developed beginning in the 15th century.

Before that, equations were written out in words

EXAMPLE For example, an algebra problem

from the Chinese Arithmetic in Nine Sections, circa 200 BCE, begins "Three sheaf's of good crop, two sheaf's of mediocre crop, and one sheaf of bad crop are sold for 29 rupee.

" We would write 3x + 2y + z = 29.

TYPES OF POLYNOMIAL

TYPES OF DEGREE OF POLYNOMIAL

S.NO Name of Polynomial

Polynomial of Degree

1) LINEAR One

2) QUATRATIC Two

3) CUBIC Three

4) BI-QUATRATIC Four

THE RELATIONSHIP BETWEEN THE ZEROESAND THE CO-EFFICIENTS OF THE QUADRATIC POLYNOMIAL.SUM OF ZEROES i.e., ALPHA+BETA = -B/A i.e., co-efficient of x/co-

efficient of x2

PRODUCT OF ZEROES i.e., ALPHA X

BETA= C/A i.e., co-efficient of constant/ co-efficient of x2

DIVISION ALGORITHMTHE FORMULA FOR DIVISOR IS

DIVIDEND INTO QUOTIENT +REMAINDER.

P(x) = G(x) X Q(x) + R(x)HEAR, G(x) is DIVIDEND Q(x) is QUOTIENT R(x) is REMAINDER P(x) is DIVISOR

POLYNOMIAL IN GRAPHPolynomial of degree 2:f(x) = x2 − x − 2= (x + 1)(x − 2)

POLYNOMIAL IN GRAPHPolynomial of degree 3:f(x) = x3/4 + 3x2/4 − 3x/2 − 2= 1/4 (x + 4)(x + 1)(x − 2)

POLYNOMIAL IN GRAPHPolynomial of degree 4:f(x) = 1/14 (x + 4)(x + 1)(x − 1)(x − 3) + 0.5

EDUCATIONAL USEWe can divide polynomials.We can multiply polynomials.We can graph the polynomials.We can even change the word

problem into expression to solve it.We can learn beyond the numbers

using it.Even though all these are difficult it

will increase thinking skill of children.

DIVISION

MULTIPLICATION

EXPRESSION

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