Page 98 - Start Up Mathematics_7

Coefficient
In an algebraic expression, coefficient is either a numerical factor, an algebraic factor or the
product of two or more factors. In the algebraic expression 10xy, 10 is the coefficient of xy, 10x
is the coefficient of y and 10y is the coefficient of x.

Like Terms
2
2
2
Terms having the same literal factors are called like terms. For example, x y, 3x y and –5x y are
like terms.
Unlike Terms
2
Terms having different literal factors are called unlike terms. For example, 3x y, 3xy and –5x 2
are unlike terms.

Monomials
2
Algebraic expressions having one term are called monomials. Examples of monomials are 3x y,
4xy and 2x.

Binomials
2
Algebraic expressions having two terms are called binomials. Examples of binomials are 3x y + 5x,
2
4xy – 6y and 2x – 7.

Trinomials
Algebraic expressions having three terms are called trinomials. Examples of trinomials are
2
3x y + 3xy + 5 and 4xy + 2x + 2.
Polynomials

Algebraic expressions having one or more terms are called polynomials. In a polynomial, power
of x is a non-negative integer. In polynomials, the variables cannot have negative of fractional
7
2
3
3
exponents for any term. Examples of polynomials are 5x + 2x, 3y – xy and . Expression of
2
8 8
–2
the type 4xy + is not a polynomial because in , i.e., 8x , the power of x is –2, which is not
x 2 x 2
a whole number.
Degree of a polynomial
The highest power of a variable in a polynomial is called the degree of the polynomial.
2
For example, (i) degree of the polynomial (x – 1)(2 – 3x) = –3x + 5x – 2 is 2.
2 3
2 3
3
(ii) degree of the polynomial x y – 7xy + 8xy + 17 is 5 (power of x y is
obtained by adding 2 and 3).
Example 1: Form algebraic expressions using variables, constants and arithmetic operations.
(a) Half of z added to x
(b) The number x multiplied by itself
(c) One-fourth of the product of numbers p and q
(d) Cube of x subtracted from product of x and y
(e) 4 added to three times the product of numbers m and n

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