1. Which of the following expressions are
polynomials in one variable and which are not?
State reasons for your answer.
(i) 4r2 – 3x + 7 (ii) y2 + 2
2
(iii) 3Vt + tv2 + (iv) y +
(v) 710 + y2 + 450
Answers
Question :-
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x^2 – 3x + 7
(ii) y^2 + √2
(iii) 3 √t + t√2
(iv) y+ 2/y
(v) x^10+ y^3+t^50
Answer :-
(i) We have 4x^2 – 3x + 7 = 4x^2 – 3x + 7x^0
It is a polynomial in one variable i.e., x
because each exponent of x is a whole number.
(ii) We have y^2 + √2 = y^2 + √2y^0
It is a polynomial in one variable i.e., y
because each exponent of y is a whole number.
(iii) We have 3 √t + t√2 = 3 √t^1/2 + √2.t
It is not a polynomial, because one of the exponents of t is 1/2,
which is not a whole number.
(iv) We have y + y+2/y = y + 2.y^-1
It is not a polynomial, because one of the exponents of y is -1,
which is not a whole number.
(v) We have x^10+ y^3 + t^50
Here, exponent of every variable is a whole number, but x^10 + y^3 + t^50 is a polynomial in x, y and t, i.e., in three variables.
So, it is not a polynomial in one variable.
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