Page 122 - Maths Skills - 7

120 Maths

So, to find the degree of an expression or a polynomial.

Step 1: Write the expression in descending order of the powers of their terms.
Step 2: Add the powers of two or more variables in the same term.
Step 3: The highest power of the term is the degree of the polynomial.
For example, in x + x – 3x + 1, the degree of the polynomial is 4.
4
2
In 2xy – 3x y + 4y – 2, the degree of the polynomial is 3.
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TYPES OF ALGEBRAIC EXPRESSIONS
The different types of algebraic expressions are as follows:

Monomial Fact-o-meter
An algebraic expression containing only one term is called a monomial.
A polynomial can have
For example, 2xy, 9ab, – 4zr, etc. are all monomials. no literal or variable in
Binomial the denominator.
5a
2
An algebraic expression containing only two terms is called a binomial. i.e. b + 7a is not a
For example, 4xy – 2, 3ab – 7x, 2x + 5 , etc. are all binomials. polynomial.
2
2
Trinomial
An algebraic expression containing only three terms is called a trinomial.

For example, p + q + r, 9a – 2b + c, 7y – 4x + 2xy, etc. are all trinomials.
3
Quadrinomials
An algebraic expression containing only four terms is called a quadrinomial.

For example, 3x – 4x + y + 2, 80b – 2bx + 4x – 7, etc. are quadrinomials.
2
2
Polynomial
The general name for an algebraic expression containing two or more terms is called polynomial, i.e., binomial,
trinomial, etc. are all polynomials.
Let us learn more through examples.

Let’s Attempt

Example 1: Identify the terms and factors in the following expressions:
(i) x – 7 (ii) 3xy – 4x + 7 (iii) 2 – y 3
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Solution: (i) x – 7 (ii) 3xy – 4x + 7
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Terms : x and – 7 Terms: 3xy, – 4x and 7
2
Factors: x and – 7 Factors: 3xy = 3 × x × y
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(iii) 2 – y 3 – 4x = – 4 × x × x
Terms : 2 and – y 3 7 = 7
Factors: 2 = 2

– y ⇒ (– y × (– y × (– y
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