Question

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$\\ \bullet\ \quad \blue{\mathbf{Is\ zero\ (0)\ a\ polynomial\ ?}}$


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Answer 1

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$\tt \: Question :$

$\quad \blue{\mathbf{Is\ zero\ (0)\ a\ polynomial\ ?}}$

$\tt \: Answer :$

Yes. Zero is a polynomial.

Polynomial is an expression that have constants, variables and exponents to solve .

The fundamental theorem of algebra states that every non-constant, single- variable polynomial with complex coefficients has at least one complex roots

This includes polynomials with real coefficients .

Terms of Polynomial :

• Degree of a Polynomial

There are Different Classification of Polynomials

1. Monomial
2. Binomial
3. Trinomial

Types of Polynomial :

1. Constant or Zero Polynomial
2. Linear Polynomial
3. Quadratic Polynomial
4. Cubic Polynomial
5. Quartic Polynomial

In the above answer, we saw that all the important notes. Now, using above methods solve the below given three question :

1. -5x² + 4x + 2

2. x ( using Degree of polynomial ) find this.

3. x¹ + 4

This includes polynomials with real coefficients .

$\sf \: Learn \: more :$

• The corresponding polynomial function is the constant function with value 0, also called the zero map .

• Formula

ax + b = 0

a is the coefficient, b is the constant and the degree of the polynomial is 1 .

Answer 2

Answer:

"Yes"! zero is a polynomial.

Explanation:

• A polynomial is an expression consisting of coefficients and variables.

In order to prove that zero is a polynomial, let us know the rules for an expression NOT to be an polynomial.

NOT a polynomial:

• The polynomials cannot contain fractional exponents.
• Polynomials cannot contain radicals.
• The exponent of a polynomial cannot be negative.
• The 'x' of the expression cannot be the exponent.
• The 'x' of the expression cannot be in the denominator.

So, as per the rules, zero (0) can be an polynomial.

OR we can simply say that zero is a constant polynomial.

$\sf{Constant\: polynomial}$: A polynomial of degree zero and contains no variable is called a constant polynomial.

$\qquad\quad\bold{\underline{\qquad\qquad\qquad\qquad\qquad\qquad}}$

Also, it is stated in the rules that "Sum of polynomial is polynomial itself."

So, for occasion let's take an expression:

$\qquad\qquad\quad\bigstar$ (3x + 2) + ( -3x + 2) = 0

Here, 3x + 2 and -3x + 2 are two polynomial in variable x. Here, the sum of two polynomial is zero. So, as per the statement and the expression we can say that zero is an polynomial.