ALGEBRAIC EXPRESSION is an expression built up from constants, variables, and the algebraic operations (addition, subtraction, multiplication, division andexponentiation by an exponent that is
a rational
number).
POLYNOMIAL is an expression consisting of variables (or indeterminates)
and coefficients, that involves only the
operations ofaddition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial
of a single indeterminate (or variable), x, isx2 − 4x + 7, which
is a quadratic polynomial.
A MONOMIAL is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly
with repetitions.
A BINOMIAL is a polynomial which is the sum of two
terms, which are monomials.[1] It is the simplest kind
of polynomial after the monomials.
A MULTINOMIAL is an algebraic expression having more than one term. For example:
9x3 + 2x2 + 5
IN ALGEBRA a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or – signs
IN ALGEBRA a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or – signs
A VARIABLE is a symbol that denotes a mathematical object, which could be
a number, a vector,
a matrix,
or even a function. In this case, the original property of
"variability" of a variable is not kept (except, sometimes, for
informal explanations).
LIKE TERMS are terms that contain the same variables raised to the same
power. Only the coefficients of like terms are
different.
UNLIKE TERMS : The terms having the same variable with different exponents or
different variable with same exponents are calledUnlike terms .
EXPONENTS are shorthand for repeated multiplication of the same thing by itself.
For instance, the shorthand for multiplying three copies of the
number 5 is shown on the right-hand side of the "equals"
sign in (5)(5)(5) = 53. The "exponent", being 3 in
this example, stands for however many times the value is being multiplied. The
thing that's being multiplied, being5 in this example, is called the
"base".
DEFINITION OF NUMERICAL COEFFICIENT -The constant multiplicative factors attached
to the variables in an expression are known as Numerical Coefficient.
FACTORS
are numbers you can multiply together to get another number:
THE PRODUCT RULE is a formal rule for differentiating problems where one function is
multiplied by another.
THE QUOTIENT RULE is a formal rule for differentiating problems where one function is
divided by another.
THE POWER RULE is one of the most important differentiation rules. Since differentiation is linear, polynomials can be differentiated
using this rule.
SYNTHETIC DIVISION is a shorthand, or shortcut, method of polynomial division in the special case of
dividing by a linear factor -- and it only works in this case.
Synthetic division is generally used, however, not for dividing out factors but
for finding zeroes (or roots) of polynomials. More about this later.
Exponents rules and properties
Rule name
|
Rule
|
Example
|
a n · a m = a n+m
|
23 · 24 = 23+4 = 128
|
|
a n · b n = (a · b) n
|
32 · 42 = (3·4)2 = 144
|
|
a n / a m = a n-m
|
25 / 23 = 25-3 = 4
|
|
a n / b n = (a / b) n
|
43 / 23 = (4/2)3 = 8
|
|
(bn)m = bn·m
|
(23)2 = 23·2 = 64
|
|
bnm =
b(nm)
|
232 =
2(32)= 512
|
|
m√(bn)
= b n/m
|
2√(26)
= 26/2 = 8
|
|
b1/n = n√b
|
81/3 = 3√8 = 2
|
|
b-n = 1 / bn
|
2-3 = 1/23 = 0.125
|
|
Zero rules
|
b0 = 1
|
50 = 1
|
0n = 0 , for n>0
|
05 = 0
|
|
One rules
|
b1 = b
|
51 = 5
|
1n = 1
|
15 = 1
|
|
Minus one rule
|
 |
(-1)5 = -1
|
Derivative rule
|
(xn)' = n·x n-1
|
(x3)' = 3·x3-1
|
Integral rule
|
∫ xndx = xn+1/(n+1)+C
|
∫ x2dx = x2+1/(2+1)+C
|
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