Question

what is the
degree of the Zero polynomial ?​

Answer 1

Answer: zero polynomial is the one where all the coefficients are equal to zero. So, the degree of the zero polynomial is either undefined, or it is set equal to -1.

Step-by-step explanation: its help

Answer 2

A polynomial’s degree is the highest or the greatest power of a variable in a polynomial equation. The degree indicates the highest exponential power in the polynomial (ignoring the coefficients).

For example: 6x4 + 2x3+ 3 is a polynomial. Here 6x4, 2x3, 3 are the terms where 6x4 is a leading term and 3 is a constant term. The coefficients of the polynomial are 6 and 2.

The degree of the polynomial 6x4 + 2x3+ 3 is 4.

Let’s take another example: 3x8+ 4x3 + 9x + 1

The degree of the polynomial 3x8+ 4x3 + 9x + 1 is 8.

We know that the polynomial can be classified into polynomial with one variable and polynomial with multiple variables (multivariable polynomial). As discussed above, the degree of the polynomial with one variable is the higher power of the polynomial expression. But, if a polynomial with multiple variables, the degree of the polynomial can be found by adding the powers of different variables in any terms present in the polynomial expression.

Let’s consider a polynomial expression with two variables, say x and y

(i.e) x3 + 6x2y4 + 3y2+5

The degree of the polynomial is 6.

Because in the second term of the algebraic expression, 6x2y4, the exponent values of x and y are 2 and 4 respectively. When the exponent values are added, we get 6. Hence, the degree of the multivariable polynomial expression is 6.

So, if “a” and “b” are the exponents or the powers of the variable, then the degree of the polynomial should be “a + b”, where “a” and “b” are the whole numbers.

Degree of a Zero Polynomial

A zero polynomial is the one where all the coefficients are equal to zero. So, the degree of the zero polynomial is either undefined, or it is set equal to -1.

Degree of a Constant Polynomial

A constant polynomial is that whose value remains the same. It contains no variables. The example for this is P(x) = c. Since there is no exponent so no power to it. Thus, the power of the constant polynomial is Zero. Any constant can be written with a variable with the exponential power of zero. Constant term = 6 Polynomial form P(x)= 6x0

How to Find the Degree of a Polynomial?

A Polynomial is merging of variables assigned with exponential powers and coefficients. The steps to find the degree of a polynomial are as follows:- For example if the expression is : 5x5 + 7x3 + 2x5+ 3x2+ 5 + 8x + 4

Step 1: Combine all the like terms that are the terms with the variable terms.

(5x5 + 2x5) + 7x3 + 3x2+ 8x + (5 +4)

Step 2: Ignore all the coefficients

x5+ x3+ x2+ x1 + x0

Step 3: Arrange the variable in descending order of their powers

x5+ x3+ x2+ x1 + x0

Step 4: The largest power of the variable is the degree of the polynomial

deg( x5+ x3+ x2+ x1 + x0) = 5

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