Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer:
(i) 3x²-4x+15
(ii) y²+2√3
(iii) 3+√x + √2x
(iv) x- 4/x
(v) x¹²+y3+t⁵⁰
Answers
(i) Given : 3x² - 4x + 15
The given expression has single variable x.
The exponent of x is whole number i.e , 2.
Hence, The given expression is a polynomial in one variable.
(ii) y² + 2√3
The exponent of y is a whole number i.e , 2.
Hence, the given expression is a polynomial in one variable.
(iii) 3 + √x + √2x
Here,the exponent of the second term is ½, which is not a whole number. Therefore, its not a polynomial.
(iv) x - 4/x
x - 4x-¹
Here the exponent of the second term is negative (-1 ), which is not a whole number.
Hence, the given expression is not a polynomial.
(v) x¹² + y3 + t⁵⁰
The expression has three variables x, y, t.
Hence, it is not a polynomial in one variable.
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Similar questions :
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^(1/2)
(iii) 3.t^(1/2) + t.2^(1/2)
(iv) y + 2/y
(v) x^10 + y^3 + t^50
Classify the following polynomials as polynomials in one-variable, two variable etc: (i) x²-xy+7y² (ii) x²-2tx+7y²-x+t (iii) t³-3t²+4t-5 (iv) xy + yz + zx
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(i) 3x²-4x+15
Number of variables: x
Thus, its a one variable polynomial
(ii) y²+2√3
Number of variables: y
Thus, its a one variable polynomial
(iii) 3+√x + √2x
Exponent of x = 1/2, which isn't a whole number
Thus, its not a polynomial
(iv) x- 4/x
Exponent of x = -1, which isn't a whole number
Thus, its not a polynomial
(v) x¹²+y3+t⁵⁰
Number of variables: x, y, t
Thus, its a three variable polynomial