Polynomials

(1) A polynomial is said to be trinomial if it contains only three term in its entire expression.

So in the given expression, we have three terms. One is x², second is -2x and the third term is 3.

So the given polynomial is a trinomial.

(2) A polynomial is said to be monomial if it contains only one term in its entire expression.

In the above polynomial, there is only one term which 8y and hence this term is a monomial.

(3) A polynomial is said to be binomial if it contains only two term in its entire expression.

So in the given expression, we have two terms. One is 2a³, second is -5 and hence this term is a binomial.

(4) A polynomial is said to be binomial if it contains only two term in its entire expression.

So in the given expression, we have two terms. One is -11b, second is 3 and hence this term is a binomial.

(5) A polynomial is said to be monomial if it contains only one term in its entire expression.

In the above polynomial, there is only one term which 17m⁴ and hence this term is a monomial.

(6) A polynomial is said to be trinomial if it contains only three term in its entire expression.

So in the given expression, we have three terms. One is 6n², second is -n and the third term is 5.

So the given polynomial is a trinomial.

(7) A polynomial is said to be trinomial if it contains only three term in its entire expression.

So in the given expression, we have three terms. One is x³, second is -7x and the third term is 35.

So the given polynomial is a trinomial.

(8) A polynomial is said to be monomial if it contains only one term in its entire expression.

In the above polynomial, there is only one term which 51 and hence this term is a monomial.

(9) A polynomial is said to be binomial if it contains only two term in its entire expression.

So in the given expression, we have two terms. One is -8y³, second is 13 and hence this term is a binomial.

(10) A polynomial is said to be trinomial if it contains only three term in its entire expression.

So in the given expression, we have three terms. One is -4p², second is 12p and the third term is 1.

So the given polynomial is a trinomial.

(1) The given algebraic expression is a polynomial in one variable because all the powers of x are whole numbers.

In this given polynomial the power of b is +2 and 0.

Hence these are whole powers of b and hence this expression is a polynomial.

(2) y^1/2 -5y + 18 is not a polynomial because in this given equation the first term contains the power of y as 1/2 where 1/2 is not a whole number. So the given algebraic expression is not a polynomial.

(3) 7/m - 2 is not a polynomial because in this given equation the second term becomes 7 × m^-1 where -1 is not a whole number. So the given algebraic expression is not a polynomial.

(1) The given algebraic expression is a polynomial in one variable because all the powers of x are whole numbers.

In this given polynomial the power of a is +2, 1 and 0.

Hence these are whole powers of a and hence this expression is a polynomial.

(2) The given algebraic expression is a polynomial in one variable because all the powers of x are whole numbers.

In this given polynomial the power of n is +3, 2 and 0.

Hence these are whole powers of n and hence this expression is a polynomial.

(3) The given algebraic expression is not a polynomial because all the powers of x are not whole numbers.

In this given polynomial the power of x is 2 and 3.5.

Hence these 3.5 is not a whole power of x and hence this expression is not a polynomial.

(4) The number -13/9 is a polynomial because 10 can be represented as follows: = 13/9 × x⁰ which is equal to -13/9. So it is a polynomial.

(5) n - 1/n is not a polynomial because in this given equation the second term becomes 1 × n^-1 where -1 is not a whole number. So the given algebraic expression is not a polynomial.

(6) The given algebraic expression is a polynomial in one variable because all the powers of x are whole numbers.

In this given polynomial the power of a is +3, 1 and 0.

Hence these are whole powers of a and hence this expression is a polynomial.

(7) The number 51 is a polynomial because 10 can be represented as follows: 51 × x⁰ which is equal to 51. So it is a polynomial.

(8) The given algebraic expression is a polynomial in one variable because all the powers of x are whole numbers.

In this given polynomial the power of b is 4, 2 and 0.

Hence these are whole powers of b and hence this expression is a polynomial.

(9) This expression can be expressed as follows:

12 + 10p²

The given algebraic expression is a polynomial in one variable because all the powers of x are whole numbers.

In this given polynomial the power of p is 2 and 0.

Hence these are whole powers of p and hence this expression is a polynomial.

For an expression to be polynomial the powers of the variable should be whole numbers.

The polynomials are as follows:

(i) 4

(ii) 2x

(iii) 2x² + 2x + 4

(iv) 2/p^-2

(v) 2z

If the powers of the variable are not whole numbers then the expression is not a polynomial.

The expressions are as follows:

(i) √x

(ii) 1/x

(iii) 1/x²

(iv) x^3.5

(v) x^-2

(1) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 23 is multiplied to x³ and hence the coefficient is 23 and the degree is 3.

(2) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 18 is multiplied to x⁰ and hence the coefficient is 18 and the degree is 0.

(3) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial -6 is multiplied to m⁵ and hence the coefficient is -6 and the degree is 5.

(4) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 11/5 is multiplied to y and hence the coefficient is 11/5 and the degree is 1.

(5) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 1 is multiplied to a² and hence the coefficient is 1 and the degree is 2.

(6) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial -10 is multiplied to n² and hence the coefficient is -10 and the degree is 2.

(7) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial -13/9 is multiplied to x⁴ and hence the coefficient is -13/9 and the degree is 4.

(8) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 4 is multiplied to y and hence the coefficient is y and the degree is 1.

(9) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 1 is multiplied to x and hence the coefficient is 1 and the degree is 1.

(10) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial -2/5 is multiplied to y³ and hence the coefficient is -2/5 and the degree is 3.

(11) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial -15 is multiplied to s³ and hence the coefficient is -15 and the degree is 3.

(12) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 18 is multiplied to z⁶ and hence the coefficient is 18 and the degree is 6.

(13) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 4 is multiplied to t⁸ and hence the coefficient is 4 and the degree is 8.

(14) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial -17 is multiplied to p and hence the coefficient is -17 and the degree is 1.

(15) Coefficient is the constant which is multiplied to the variable and degree represent the power of the variable.

In the monomial 7/9 is multiplied to q⁸ and hence the coefficient is 7/9 and the degree is 8.

(1) The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients.

This algebraic expression has two powers 3 and 1.

So the highest power is 3 and hence the degree of the polynomial is 3.

(2) The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients.

This algebraic expression has two powers 2, 1 and 0.

So the highest power is 2 and hence the degree of the polynomial is 2.

(3) The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients.

This algebraic expression has two powers 4, 1 and 0.

So the highest power is 4 and hence the degree of the polynomial is 4.

(4) The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients.

This algebraic expression has two powers 1.

So the highest power is 1 and hence the degree of the polynomial is 1.

(5) The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients.

This algebraic expression has two powers 0.

So the highest power is 0 and hence the degree of the polynomial is 0.

(6) The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients.

This algebraic expression has two powers 5, 3, 2, and 0.

So the highest power is 5 and hence the degree of the polynomial is 5.

(7) The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients.

This algebraic expression has two powers 5 and 0.

So the highest power is 5 and hence the degree of the polynomial is 5.

(8) The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients.

This algebraic expression has two powers 4 and 1.

So the highest power is 4 and hence the degree of the polynomial is 4.

(9) The degree of the zero polynomial is left to be undefined.

Hence its degree cannot be defined.

The polynomial is as follows:

x³ + 3x² + 3x + 3

The polynomial is as follows:

y⁴ + y³ + 3y² + 3y + 3

The polynomial is as follows:

3a + 3

The polynomial is as follows:

m⁵ + m⁴ + m³ + 3m² + 3m + 3