⇒ What is polynomial (POLYNOMIAL)?
The group of terms of the variable and constant are called polynomials.
Like – x² + 2x + 2
⇒ Classification of Polynomial: –
(a) Monomial: An expression that has only 1 term is called a monomial polynomial.
Such as -9x, 2x, 7x², 4 etc.
(b) Binomial or Binomial Polynomial: – An expression which has only 2 terms is called a monomial polynomial.
Eg -7 x² + 2, 3-8x etc.
(c) Tripod or Trinomial: – The expression which has only 3 terms is called Ekapadi polynomial.
Like -7x² + 2x -3, 3x³-8x + 2 etc.
(d) Zero Polynomial: – A polynomial with zero coefficient is called zero (0) polynomial.
Eg -0.x²-o.x + 0 etc
The polynomial power of zero is indeterminate.
⇒ Classification of multiple terms based on exponent of variables used in multiples.
(a) Linear polynomial: – The polynomial whose maximum power is 1. It is called linear polynomial.
Like -4x, 3x, x etc
(b) Quadratic polynomial: – The polynomial whose maximum power is 2. It is called linear polynomial.
Eg -4 x²3x, 3x², x²etc
(c) Cubic polynomial: – The polynomial whose maximum power is 3. It is called linear polynomial.
Eg -4 x³ + 4x, 3x³ + 3x² + 4x + 5, x³etc
⇒ Partition rules
p (x) = g (x) .q (x) + r (x)
Dividend = divisor × quotient + remainder
⇒ Formulas for factorization of multiple terms
1 (a + b) ² = a² + b² + 2ab
2 (a + b) ² = (a + b) (a + b)
3 (a-b) ² = a² + b²-2ab
4 (a-b) ² = (a + b) (a-b)
5 (a + b + c) ² = a² + b² + c² + 2ab + 2bc + 2ca
6 (a + b + c) ² = (a + b + c) (a + b + c)
7 (a + b) ³ = a³ + b³ + 3ab (a + b)
8 (a + b) ³ = a³ + b³ + 3a²b + 3ab²
9 (a-b) ³ = a³-b³-3a²b + 3ab²
10 (a-b) ³ = a³-b³-3ab (a-b)
11 a² + b² = (a-b) ² + 2ab
12 (a + b) ² = (a-b) ² + 4ab
13 (a-b) ² = (a + b) ²-4ab
14 a³-b³ = (a-b) (a² + b² + ab)
15 a³ + b³ = (a + b) (a² + b²-ab)
16 a³ + b³ + c³-3abc = (a + b + c) (a² + b² + c²-ab-bc-ca)
17 a³ + b³ + c³-3abc = ½ (a + b + c) (a-b) ² + (b-c) ² + (c-a) ²
Laws of Indices