Which
of the following expressions are polynomials in one variable and which
are not? State reasons for your answer.
(i) 4x2 – 3x + 7 (ii) y2 + √2 (iii) 3√t + t√ 2 (iv) y +2/y (v) x10 + y3 + t50
Solution (i)4x2 – 3x + 7
there is only one variable x with whole number power so this polynomial in one variable
(ii)y2 + √2
there is only one variable y with whole number power so this polynomial in one variable
(iii) 3√t + t√ 2
there is only one variable t but in 3√t power of t is ½ which is not a whole number so 3√t + t√ 2 is not a polynomial
(iv)y +2/y
there is only one variable y but 2/y = 2y-1 so the power is not a whole number so y +2/y is not a polynomial
(v) x10 + y3 + t50
there are three variable x y and t and there powers are whole number so this polynomial in three variable
(i) 4x2 – 3x + 7 (ii) y2 + √2 (iii) 3√t + t√ 2 (iv) y +2/y (v) x10 + y3 + t50
Solution (i)4x2 – 3x + 7
there is only one variable x with whole number power so this polynomial in one variable
(ii)y2 + √2
there is only one variable y with whole number power so this polynomial in one variable
(iii) 3√t + t√ 2
there is only one variable t but in 3√t power of t is ½ which is not a whole number so 3√t + t√ 2 is not a polynomial
(iv)y +2/y
there is only one variable y but 2/y = 2y-1 so the power is not a whole number so y +2/y is not a polynomial
(v) x10 + y3 + t50
there are three variable x y and t and there powers are whole number so this polynomial in three variable
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