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A polynomial is a mathematical expression consisting of variables, co-efficient, and the operations of addition, subtraction, multiplication. and non-negative integer exponents.
COMPONENTS OF POLYNOMIALS
COMPONENTS OF POLYNOMIALS
-> The 'building blocks' of polynomials are called monomials.
-> A monomial is a polynomial expression that contains variables and a co-efficient and does not contain addition and subtraction.
-> Monomials are often called terms if they are a part of a larger polynomial.
-> They are separated by (+) or (-).
CO-EFFICIENT - The co-efficient of a term is the non-variable factor of that term.
DEGREE OF POLYNOMIALS
DEGREE OF POLYNOMIALS
-> Polynomials are often classified by degrees.
-> The degree of a monomial is the sum of the exponents of each variable in the monomial.
-> The degree of a polynomial is the largest degree out of all the degrees of monomials in the polynomials.
->Degree of a constant polynomial is Zero.
CONSTANT POLYNOMIAL
CONSTANT POLYNOMIAL
DEGREE (0)
LINEAR POLYNOMIAL
LINEAR POLYNOMIAL
DEGREE (1)
QUADRATIC POLYNOMIAL
QUADRATIC POLYNOMIAL
DEGREE (2)
CUBIC POLYNOMIAL
CUBIC POLYNOMIAL
DEGREE (3)
QUARTIC POLYNOMIAL
QUARTIC POLYNOMIAL
DEGREE (4)
ARITHMETIC ON POLYNOMIAL
ARITHMETIC ON POLYNOMIAL
(3x^2 - 2x + 4) + (-3x^2 + 6x - 10)
= 3x^2 - 2x + 4 - 3x^2 + 6x - 10
= (3x^2 - 3x^2) + (-2x + 6x) + (4 - 10)
= 4x - 6
(2x^3 + x^2 + x + 1) - (2x^2 + 3x + 4)
= 2x^3 + x^2 + x + 1 - 2x^2 - 3x - 4
= 2x^3 + (x^2 - 2x^2) + (x - 3x) + (1 - 4)
= 2x^3 - x^2 - 2x - 3
VALUE OF POLYNOMIAL
VALUE OF POLYNOMIAL
p(x) = x^2 -3x - 4 x = -1
p(-1) = (-1)^2 - 3 * (-1) - 4
= 1 + 3 - 4
= 0
ZERO OF A POLYNOMIAL p(x)
ZERO OF A POLYNOMIAL p(x)
Zero of a polynomial can be defined as the points where the polynomials becomes zero as a whole.
eg :- p(x) = 2x + 3
=> 2x + 3 = 0
=> x = -3/2
-> -3/2 is the zero of the polynomial 2x + 3.
THE GEOMETRICAL MEANING OF A ZERO OF A QUADRATIC POLYNOMIAL
THE GEOMETRICAL MEANING OF A ZERO OF A QUADRATIC POLYNOMIAL
OPENING UP
OPENING UP
OPENING DOWN
OPENING DOWN
From our observation earlier about the shape of the graph of (y = ax^2 + bx + c). The following three cases can happen
From our observation earlier about the shape of the graph of (y = ax^2 + bx + c). The following three cases can happen
CASE 1
CASE 1
The graph cuts x-axis at two distinct points A and A'.
CASE 2
CASE 2
The graph cuts the x-axis exactly at one point, i.e. at two coincident points.
CASE 3
CASE 3
The graph is either completely above the x-axis or completely below the x-axis. so, it does not cut the x-axis at any point.
RELATION BETWEEN ZEROES AND THE CO-EFFICIENT OF A POLYNOMIAL
RELATION BETWEEN ZEROES AND THE CO-EFFICIENT OF A POLYNOMIAL
UNDERSTAND BETTER
UNDERSTAND BETTER
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