Polynomial Important Formula Class 9

Here are polynomial formula class 9 to solve polynomial equations in effective way.

What is Polynomials ?

“A polynomial is an algebraic expression in which the variables have non-negative integral exponents only” . Ex- 4×2+8y-9, -9×2+31×2+9x+1

What is Degree of polynomials ?

The Degree of polynomial define as the highest exponent of the variable in a polynomial is known as the degree of polynomial.

Types of Polynomials:

Linear Polynomial:

It is the polynomial of degree one and it is in the form of ax + b, where a & b are the real numbers with a ≠ 0.

Example: 9x + 1

Quadratic Polynomial:

Quadratic polynomial define as a polynomial of degree two and in the form of ax2 + bx + c, where a, b, c are real numbers with a ≠ 0. 

Example- 12×2 + 9x – 10

Cubic Polynomial:

A polynomial of degree three and in the form of ax3 + bx2 + cs + d, where a, b, c and d are real numbers with a ≠ 0. 

Example- 10y3 + 12x.

Zero Polynomial:

A polynomial having a degree zero. 

Example:-10x°

More types: Monomial, Binomial, Trinomial:

• Monomial: Polynomial having only one term. Example→x10, 30z
• Binomial: Polynomial having one two terms. Example →2z + 21
• Trinomial: Polynomial having only three terms. Example→ 2×2 + 51x + 20

What is Remainder Theorem ?

The remainder theorem states that if a polynomial P(x) is divided by linear polynomial q(x), then the degree of the remainder must be zero i.e. it has to be constant which may be zero.

Dividend = Divisor × Quotient + Remainder

What is Factor Theorem?

Factor theorem determines whether a polynomial q(x) is a factor of a polynomial q(x) or not without performing the actual division.

Let P(x) be a polynomial.

P(a) = 0, then x = a or (x – a) is a factor of P(x). Conversely if (x – a) is a factor of P(x), then P(a) = 0

Top 10 Algebraic Identities are:

1. (x + y)² = x² + 2xy + y²
2. (x – y)² = x² – 2xy + y²
3. (x + y) (x – y) = x² – y²
4. (x + a) (x + b) = x² + (a + b) x + ab.
5. (x + a) (x – b) = x² + (a – b) x – ab.
6. (x – a) (x + b) = x² + (b – a) x – ab.
7. (x + y + z)² = x² + y² + z2 + 2xy + 2yz + 2zx
8. (x + y)³ = x³ + y³ + 3xy(x + y)
9. (x – y)³ = x³ – y³ – 3xy(x – y)
10. x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx)

Must see: CBSE Board Half Yearly Exam Class 10 English Updated Question Paper 2022-23