Chapter 2 - Polynomials
The easiest way to understand the chapter!
An expression containing variables, constant and any arithmetic operation is called polynomial. Polynomial comes from ‘poly’ means ‘many’ and ‘nominal’ means ‘terms,’ so we can also say “many terms.”
Polynomials are of three types:
· Monomial = a polynomial which contains only one term, for example, = 3xy2
· Binomial = a polynomial which contains two terms, for example, = 5x-1
· Trinomial = a polynomial which contain three term for example = 3x2 + 5y-3
The ScoreXTM provides the best study material for CBSE Class 10 maths polynomial chapter to get the desired results.
What is the format of the course?
In the course of CBSE class 10 math chapter 2, we cover all the main topics given in the school book. Some are:-
1. Some basic terms.
• Degree of the polynomial: - The highest power of the variable in a polynomial is termed as the highest degree of the polynomial.
• Constant polynomial: - A polynomial of degree zero is called constant polynomial.
• Linear polynomial: - A polynomial of degree one E.g.:- 5x+1
• Quadratic polynomial: - A polynomial of degree two E.g.:- 6x2-4x+1
• Cubic polynomial: - A polynomial of degree three E.g.:- 3x3+6x2-4x-15
• Bi-quadratic polynomial: - A polynomial of degree four E.g.:-24x4 +15x3 - 3x2 +x+1
2. What is the Standard form?
The standard form for writing a polynomial put the terms with the highest degree first.
3. What is Factor Theorem?
Let p(x) be a polynomial of degree n>1 and let ‘a’ be any real number. If p (a) =0 then (x-a) is a factor of p(x)
PROOF: - By the reminder theorem, p(x) = (x-a) q(x) + p (a)
1 if p (a) = 0 then p(x) = (x-a) q(x) which shows that x-a is a factor of p(x)
2 x-a is factor of p(x)
P(x) = (x-a) g(x) for same polynomial g(x)
So, p (a) = (a-a) g (a) =0
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