Which of the following is a polynomial?(a). x ^ 2 - 5x + 4sqrt(x) + 3 (c). sqrt(x) + 1/(sqrt(x)) (b). x ^ (3/2) - x + x ^ (1/2) + 1 (d). sqrt(2) * x ^ 2 - 3sqrt(3) * x + sqrt(6)
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Which of the following expressions are polynomials? Justify your answer:
(i) 8
(ii)
3
x
2
−2x
(iii) 1−
5x
(iv)
5x
−2
1
+5x+7
(v)
x
(x−2)(x−4)
(vi)
x+1
1
(vii)
7
1
a
3
−
3
1
a
2
+4a−7
(viii)
2x
1
Medium
Solution
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Correct option is B)
A polynomial can have constants, variables and exponents, but never division by a variable.
A polynomial can't have a negative exponent.
Polynomials can have no variable at all, or one variable or two or more variables.exponents can only be 0,1,2 or multiples not in fractions.
Based on above definition, (iii) 1−
5x
is not polynomial because it's exponent is in fraction.
(v)
x
(x−2)(x−4)
, (vi)
x+1
1
& (viii)
2x
1
are not polynomials because have negative exponent.
Hence, the polynomials are: (i), (ii), (iv), (vii)