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
Answer:
I have attached the explanation.
Hope it will help you.
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.