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State reason for your answer.

i)\(4x^2 - 3x + 7\)

ii)\(y^2 + \sqrt{2}\)

iii)\(3\sqrt{t} + t\sqrt{2}\)

iv)\(y + \frac{2}{y} \)

v)\(x^{10} + y^3 + t^{50}\)

Answer :

i) \(4x^2 - 3x + 7\) is a polynomail in one variable. As it is having only non-negative integral powers of x.

ii)\(y^2 + \sqrt{2}\) is also a polynomial in one variable. As it is having only non-negative integral power of y.

iii)\(3\sqrt{t} + t\sqrt{2}\) is not a polynomial. As the integral power of the variable is not a whole number.

iv)\(y + \frac{2}{y} \) is not a polynomial. As it having a negative integral power of y.

v) \(x^{10} + y^3 + t^{50}\) is a polynomial with three variables.

- Write the coefficients of \(x^2\) in each of the following :i)\(2 + x^2 + x\)ii)\(2 - x^2 + x^3\)iii)\(\frac{\pi{x^2}}{2} + x\)iv)\(\sqrt{2}x - 1\)
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