Question

write the degree of each of the following polynomial explain me because this is my starting I don't understand

please explain me properly
nd

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Answer 1

Answer:

(i) Degree 1

(ii) Degree 2

(iii) Degree 2

(iv) Degree 5

(v) Degree 2

(vi) Degree 2

Step-by-step explanation:

Take an example of (iv) There are total 5 degrees ( 5,5,3 and 3) So the highest degree which is 5 is the degree of the Polynomial.

So, the highest degree in the polynomial is the degree of the polynomial.

Note : Like (i) there was no degree, so it is degree 1.

If there is a constant, take an example of 1, so the degree will be 0.

I hope you understood.

Answer 2

Answer:

i) 3

ii) 3

iii) 4

iv) 6

v) 3

vi) 3

Step-by-step explanation:

Polynomial: A polynomial is an expression containing variables and coefficients, and non-negative integer exponents of variables.

Degree of Polynomial with more than one variable: In the case of a polynomial with more than one variable, the degree can be found by noticing at each monomial within the polynomial, adding together all the exponents within a monomial, and choosing the largest sum of exponents. That sum is the degree of the polynomial.

e.g

i)xy + yz + zx + 3xy is a polynomial with more than one variable.

$\therefore$ Degree of the polynomial is .....

x¹y¹ = 1 + 1 = 2

y¹z¹ = 1 + 1 = 2

z¹x¹ = 1 + 1 = 2

3x¹y¹z¹ = 1 + 1 + 1 = 3

Hence the Degree of Polynomial is 3.

Solution:

ii) a² + b² + c² - 3abc

a² = 2

b² = 2

c² = 2

3a¹b¹c¹ = 1 + 1 + 1 =3

Hence the Degree of Polynomial is 3.

iii) 2xy + 3xy² + 5x²y + 7x²y²

2x¹y¹ = 1 + 1 = 2

3x¹y² = 1 + 2 = 3

5x²y¹ = 2 + 1 = 3

7x²y² = 2 + 2 = 4

Hence the Degree of Polynomial is 4.

iv)

${a}^{5} - {b}^{5} - 2 {a}^{3} {b}^{3} \\ \\ {a}^{5} = 5 \\ \\ {b}^{5} = 5 \\ \\ 2 {a}^{3} {b}^{3} = 3 + 3 = 6$

Hence the Degree of Polynomial is 6.

v) x²y + xy² + 5xy

x²y = 2 + 1 = 3

xy² = 1 + 2 = 3

5x¹y¹ = 1 + 1 = 2

Hence the Degree of Polynomial is 3.

vi) 1 + 2x + 5x²y + 6yz²

1 = Hence there are no variable so, the degree of this monomial is 0 .

2x¹ = 1

5x²y¹ = 2 + 1 = 3

6yz² = 1 + 2 = 3

Hence the Degree of Polynomial is 3.