Question

Write whether the following statements are True or False Justify you answer
(I)A binomial can have at the most two terms
(ii). Every polynomial is a binomial
(iii) A binomial may have degree 3
( iv) Degree of zero polynomial is zero
(v) The degree ofx2 +2xy+y2 is 2
(vi)πr2 is monomial
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Answer 1

(i) False

Because a binomial has exactly two terms.

(ii) False

Because a polynomial can be monomial, binomial, trinomial, etc.

For example:

x

5 + x + 1 is a polynomial but not a binomial.

(iii) True

Because the degree of a polynomial is a whole number. So, degree can be 3 also.

(iv) False

Because zero of a polynomial can be any real number.

(v) False

It may be less than or equal to 2.

For example:

Case: I

x

2+ 1 and – x

2 + 2x2 + 3 are two polynomials of degree 5 but the degree of the

sum of the two polynomials is 2.

Case: II

x

2 + 1 and x

2 + 2x2 + 3 are two polynomials of degree 5 but the degree of the sum

of the two polynomials is 2

(vi). true

Monomial is a expression with only one term. And its a type of polynomial . A polynomial consist of real numbers which include both rational and irrational numbers. πr^2 is a monomial because pi Or π is a irrational number.

Answer 2

The given questions can be solved using the concepts of Algebra.

Statement (i)

• The given statement is false because for an expression to become a binomial is should contain definitely two terms.
• Hence, Statement 1 is FALSE.

Statement (ii)

• The given statement is false, a polynomial can contain any number of terms whereas a binomial should contain only 2 terms.
• Hence, Statement 2 is FALSE.

Statement (iii)

• The given statement is true, a binomial can have any number of degrees but the number of terms must be 2. The Degree of the polynomial is not considered for deciding a binomial.
• Hence, Statment 3 is TRUE.

Statment (iv)

• The given statement is true, the degree of zero polynomial is always zero. It is considered a zero-degree polynomial.
• Hence, statement 4 is TRUE.

Statement (v)

• The given statement is true, for an expression with multiple degrees, the one highest degree is considered the degree of the polynomial
• Hence, statement 5 is TRUE.

Statement (vi)

• The given statement is true because there is only a single term r. pi is a constant. Hence, it is a monomial.

• Hence, statement 6 is TRUE.