Learner Guide : : 7
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lConstant: Quantity which has a fixed
numerical value e.g. 0, 1, 2 ....
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lVariable: Quantity which can take different
numerical values .A variable is represented by
a letter of the English alphabet such as a, b, c,
x, y, z etc.
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lAlgebraic expressions: A combination of
constants and variables, connected by any
or all of the four fundamental operations
(+, -, ×, ÷).
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lTerm: Each part of the expression alongwith
its sign
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lMonomial: An algebraic expression containing
one term eg 6a2, 3x2y2 etc.
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lBinomial: An algebraic expression containing
two terms e.g. a2 + b2, 7xy + y2 etc.
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lTrinomial: An algebraic expression containing
three terms e.g. x2 + y2 + z2, x2 + 2xy + y2 etc.
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lPolynomial: An algebraic expression in which
variable(s) does (do) not occur in the
denominator, exponents of variables are whole
numbers and numerical cofficients of various
terms are real numbers e.g. x3 – 2y2 + y –
7
is
a polynomial while x3 –
1
x
is not a polynomial.
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lFactor: When two or more numbers or
variables are multiplied, then each one of them
and their product is called a factor of the
product. A constant factor is a numerical factor
while a variable is known as a literal factor.
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lCoefficient: In a term any one of the facotrs
with the sign of the term is the coefficient of the
product of the other factors e.g. in –3xy,
cofficient of x is –3y.
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lConstant Term: Term which has no literal
factor e.g. in 2x + 9y + 7 the constant term is 7.
3
ALGEBRAIC EXPRESSIONS AND POLYNOMIALS
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lLike and Unlike Terms: Terms having same
literal factors are called like or similar terms and
terms having different literal factors are called
unlike terms.
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lDegree of a polynomial : Sum of the
exponents of the variables in a term is called
degree of the term.
Degree of a polynomial is the same as the
degree of its term or terms having the highest
degree and non-zero coefficient.
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lQuadratic polynomial : A polynomial of
degree2 e.g. x2 – 3x + 2.
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lZero degree polynomial: Degree of a non-
zero constant polynomial is taken as zero
Zero polynomial : When all the coefficients of
variables in the terms of a polynomial are zeros,
the polynomial is called a zero polynomial and
the degree of zero polynomial is not defined.
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lZeros of a polynomial: Value(s) of the variable
for which the value of a polynomial in one
variable is zero.
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lAddition and subtraction of polynomials:
The sum of two (or more) like terms is a like
term whose numerical coefficient is the sum of
the numerical coefficients of the like terms
The difference of two like terms is a like term
whose numerical coefficient is the difference of
the numerical coefficients of the like terms
To add polynomials, add their like terms together
e.g.
2x 3x 5x
+ =
,
2 2 2
3x y 8x y 11x y
+ =
To subtract a polynomial from another
polynomial subtract a term from a like term e.g
2 2 2 2 2 2
9x y 5x y 4x y
− =
,
5y 2y 3y
− =
.
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lMultiplication of the polynomials: To multiply
a monomial by a monomial, use laws of
