Chapter 2 · Class 9 CBSE · Formula Sheet
Polynomials Formulas — Class 9 CBSE
Understand degree, zeroes of polynomials, remainder theorem, and factor theorem.
Key Formulas
Degree of Polynomial
\text{Highest power of the variable}
Remainder Theorem
p(x) \div (x - a) \text{ gives remainder } p(a)
Factor Theorem
\text{If } p(a) = 0, \text{ then } (x - a) \text{ is a factor of } p(x)
Identity 5
(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
Identity 6
(a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2
Identity 7
(a - b)^3 = a^3 - b^3 - 3a^2b + 3ab^2
Sum of Cubes
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
Difference of Cubes
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Identity 8
a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)
Special Case
\text{If } a + b + c = 0, \text{ then } a^3 + b^3 + c^3 = 3abc
Worked Examples
1Using: Linear Equation
Solve 3x + 5 = 20.
Step 1: 3x = 20 - 5 = 15.
Step 2: x = 15 / 3 = 5.
Answer: x = 5
2Using: Algebraic Identity
Expand (a + 3)^2.
Step 1: Using (a + b)^2 = a^2 + 2ab + b^2
Step 2: = a^2 + 6a + 9.
Answer: a^2 + 6a + 9
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