Algebra :
Introduces the concept of variables, which allows
an unknown quantity to be represented by a alphabets to manipulation in
applications.
Algebraic expression: an expression which has variable (
alphabets), constant , operations ( addition ,subtraction,multiplication division )and exponents. We try to understand relation between two different
values of a statement .
For example
3 times of x means
( statement ) 3x( expression)
45 increased by some 6x ……… 45+6 x
30 decreased by some 2x ………30-2x
Types of Polynomials on the basis of degree:
Linear Polynomial: A polynomial of degree 1 is called a linear polynomial.Linear equations contains variable and constant , variables (x , y etc )does not have Exponents, square roots,and cube roots.
Example :2(x - 1) + 3(7x) - 10
Quadratic Polynomial: A polynomial of degree 2 is called a quadratic polynomial.
Example: ax2 + bx + c
Cubic Polynomial: A polynomial of degree 3 is called a cubic polynomial.
Bi-quadratic Polynomial: A polynomial of degree 4 is called a biquadratic polynomial
Types Algebraic expressions:
Monomial , binomial , trinomial and multinomial expressions
Monomial Expression: An Algebraic expression with single
term .
Example: 2x+3x …..x is only variable(addition with monomial with monomial)
4xy - 3xy.....x and y are variables(subtraction with monomial with monomial )
(3xy)(2x+5x) ......x and y are variables ( multiplication with monomial with binomial)
4xy - 3xy.....x and y are variables(subtraction with monomial with monomial )
(3xy)(2x+5x) ......x and y are variables ( multiplication with monomial with binomial)
Binomial Expression: An algebraic expression with two terms
,
Examples : (5x+6y) +4x ……x
and y are variables(addition binomial with monomial )
(3a - 2b ) - (2a-2b)……a and b are variables. (subtraction with binomial with binomial)
b3/2 * c/3……..b and c are variables.
Trinomial Expression : An algebraic expression with three
terms,
Examples: (3x+2y-7xy) +(2x+3y+5xy)…..X and Y are variables(addition)
( 2a+ 5a
+ 7) - (a+3a+4) …… a is the only variable(subtractions)
(xy)(x+y+z) ………..x ,y and z are
variables (multiplication)
Multinomials: An
algebraic expression with one ,two or more than terms.
Examples:
m + 5mn – 7mn + nm
3 + 5x- 4xy + 5xy
Polynomials:m + 5mn – 7mn + nm
3 + 5x- 4xy + 5xy
An algebraic expression, in which
variable(s) does (do) not occur in the denominator,
exponents of variable(s) are
whole numbers and numerical coefficients of various
terms are real numbers, is called a polynomial.Types of Polynomials on the basis of degree:
Linear Polynomial: A polynomial of degree 1 is called a linear polynomial.Linear equations contains variable and constant , variables (x , y etc )does not have Exponents, square roots,and cube roots.
Example :2(x - 1) + 3(7x) - 10
Quadratic Polynomial: A polynomial of degree 2 is called a quadratic polynomial.
Quadratic Equation: aX2
+ bx + c = 0
Example: ax2 + bx + c
Cubic Polynomial: A polynomial of degree 3 is called a cubic polynomial.
Bi-quadratic Polynomial: A polynomial of degree 4 is called a biquadratic polynomial
Algebraic equations : An algebraic expression is separated by equal to( = ), that means left hand side and right hand side. Algebra equation contains the terms like numbers, integers, fractions, roots, exponents etc. Linear equations and quadratic equations are the example of the algebraic equations.
