What is a polynomial?+ all formula

what is a polynomial

⇒ 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

(i) {{a}^{m}}\times {{a}^{n}}={{a}^{\left( m+n \right)}}

(ii) \frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{\left( m-n \right)}}

(iii) {{\left( {{a}^{m}} \right)}^{n}}='{{a}^{m\times' n}}

(iv) a{}^{-m}=\frac{1}{{{a}^{m}}}

(v) {{\left( \frac{a}{b} \right)}^{m}}=\frac{{{a}^{m}}}{{{b}^{m}}}

(vi) {{\left( ab \right)}^{m}}={{a}^{m}}{{b}^{m}}

(vii) {{a}^{m}}\times {{b}^{m}}={{\left( a\times b \right)}^{m}}

(viii) {{a}^{0}}={{a}^{m-m}}=\frac{{{a}^{m}}}{{{a}^{m}}}=1

Choose your lesson

What is a real number?

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