Q2 of 86 Page 32

Which of the following expressions are polynomials in one variable and which are not? Give reasons for your answer.

(i) 3x2 - 2x + 5


(ii) x2 + √2


(iii) p2 - 3p + q


(iv)


(v)


(vi) x100 + y100

(i) 3x2 - 2x + 5 has only one variable that is x.


∴ yes, it is a polynomial in one variable.


(ii) x2 + √2 has only one variable that is x.


∴ yes, it is a polynomial in one variable.


(iii) p2 – 3p + q has two variables that are p and q.


∴ no, it is not a polynomial in one variable.


(iv) has a negative exponent of y.


∴ no, it is not a polynomial.


(v) The exponent of x in 5√x + x√5 is 1/2 which is not a non-negative integer


∴ no, it is not a polynomial.


(vi) x100 + y100 has two variables that are x and y.


∴ no, it is not a polynomial in one variable.


More from this chapter

All 86 →
1

Find the degree of each of the polynomials given below

(i) x5 - x4 + 3


(ii) x2 + x - 5


(iii) 5


(iv) 3x6 + 6y3 - 7


(v) 4 - y2


(vi) 5t - √3

 3

Write the coefficient of x3 in each of the following

(i) x3 + x + 1 (ii) 2 - x3 + x2


(iii) (iv) 2x3 + 5


(v) (vi)


(vii) 2x2 + 5 (vi) 4

 4

Classify the following as linear, quadratic and cubic polynomials

(i) 5x2 + x - 7 (ii) x - x3


(iii) x2 + x + 4 (iv) x - 1


(v) 3p (vi) πr2

 5

Write whether the following statements are True or False. Justify your 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 of x2 + 2xy + y2 is 2


(vi) πr2 is monomial.