Q. 24.1( 13 Votes )

# State which of the following statements are true and which are false? Give reasons for your choice.

(i) The degree of the polynomial is

(ii) The coefficient of x2 in the polynomial p(x) = 3x^{3} – 4x^{2} + 5x + 7 is 2.

(iii) The degree of a constant term is zero.

(iv) is a quadratic polynomial.

(v) The degree of a polynomial is one more than the number of terms in it.

Answer :

(i) False

Since, Degree of a polynomial is the highest power of x in the polynomial which is 2 in.

(ii) False

A coefficient is a multiplicative factor in some term of a polynomial. It is the constant written before the variable.

∴ The coefficient of x^{2} is -4.

(iii) True

Since, the power of x of a constant term is 0.

∴ the degree of a constant term is 0.

(iv) False

For an expression to be a polynomial term, any variables in the expression must have whole-number powers (i.e., x^{0}, x^{1}, x^{2},……)

Since, the power in the expression has powers -2 and -1 which are not whole numbers, therefore, is not a polynomial.

(v) False

Degree of a polynomial is the highest power of x in the polynomial. The degree of polynomial is not related to the number of terms in the polynomial.

Therefore, the statement is false.

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State which of the following statements are true and which are false? Give reasons for your choice.

(i) The degree of the polynomial is

(ii) The coefficient of x2 in the polynomial p(x) = 3x^{3} – 4x^{2} + 5x + 7 is 2.

(iii) The degree of a constant term is zero.

(iv) is a quadratic polynomial.

(v) The degree of a polynomial is one more than the number of terms in it.

AP- Mathematics