Question

Which of the following is polynomials? Justify your answer.
i)√2x-1
ii) x²+3x3/2÷√x
iii) x-1÷x+1

Answer 1

Answer:

Step-by-step explanation:

a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

(i) $\sqrt{2x} -1$  = $(2x)^{1/2} -1$ which is not a polynomial as it has power 1/2 on x.

(ii)

$x^{2} +\frac{x^{\frac{3}{2} } }{x^{\frac{1}{2} } } \\= x^{2} + x^{\frac{3}{2} -{\frac{1}{2} }} \\= x^{2} + x^{\frac{2}{2} }\\= x^{2} +x^{1} \\= x^{2} +x$[Using x^a/x^b = x^(a-b) ]

It is a polynomial as it has a non-negative whole exponent on the variable.

(iii) It is not a polynomial as it has power -1 on x+1.

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