Math, asked by Anonymous, 14 hours ago

Polynomials Class 9

Explain following points
➝ A constant , A variable
➝ Coefficient
➝ Zero polynomial
➝ Terms of the polynomial
➝ Explain Remainder theorem

Explain this statement clearly

➝ The degree of a non - zero constant Polynomial is zero. ​

Answers

Answered by avantikaroy978
31

Answer:

I have attached the explanation.

Hope it will help you.

Attachments:

ImperialGladiator: Well explained! ✨
Aryan0123: Nice answer !
Answered by Aryan0123
123

Solution:

Constant:

A constant is a finite number which is not attached with any variables.

Example: 7, 19, 26, 49, etc

Variable:

A variable is an unknown quantity usually denoted by alphabets x or y.

Example: 4x, 15y, 38x², etc

Coefficient:

Coefficient is the number which is attached with variable.

Example:

  • 4 in 4x
  • 15 in 15y
  • 38 in 38x²

Zero polynomial:

When the sum of all terms in a polynomial is zero, then such a polynomial is said to be a zero polynomial.

Mathematically,

p(x) = 0

Example: Suppose polynomial p(x) → 4x - 8

So, 4x - 8 = 0

➝ 4x = 8

➝ x = 2

Terms of the polynomial:

A polynomial can be expressed as sum of monomials.

Each monomial is known as terms of the polynomial.

Example: Consider a polynomial 3x³ + 8x² + 2x = 0

Here terms of the polynomial are:

  • 3x³
  • 8x²
  • 2x

Remainder theorem:

When polynomial p(x) is divided by another polynomial g(x) then equate g(x) to zero.

So, remainder could be obtained by substituting this value of x in p(x)

Example: p(x) = 5x³ - 3x² + 2x

g(x) = 4x - 8

4x - 8 = 0

→ x = 2

p(x) = 5x³ - 3x² + 2x

p(2) = 5(2)³ - 3(2)² + 2(2) = 40 - 12 + 4 = 32

∴ Remainder = 32

The degree of a non-zero constant Polynomial is zero.

A non-zero constant polynomial can be considered as any number.

Take 9 for instánce.

9 can be written as 9x⁰.

So the degree (power) of a non-zero constant polynomial is zero.


SachinGupta01: Nice answer!
Aryan0123: Thank you ☺️
Eutuxia: Amazing! :D
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ImperialGladiator: Well explained! ✨
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Anonymous: Nicee!
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