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Types of Polynomials

Which of the ...

Question

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 $\sqrt{3}$

(iii) $3 \sqrt{x} + \sqrt{2} x$

(iv) $x - \frac{4}{x}$

(v) x¹² + y³ + t⁵⁰

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Solution

(i) is a polynomial of degree 2.i.e Quadratic polynomial.
(ii) is a polynomial of degree 2 in y variable. i.e. Quadratic polynomial.
(iii)
It is not a polynomial because exponent of x is 1/2 which is not a positive integer.
(iv)
It is not a polynomial because is fractional part.
(v)
It is a polynomial in three variables x, y and t.

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\sqrt{3}

3 \sqrt{x} + \sqrt{2} x

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Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer:

(i) $3 x^{2} - 4 x + 15$

(ii) $y^{2} + 2 \sqrt{3}$

(iii) $3 \sqrt{x} + \sqrt{2} x$

(iv) $x - \frac{4}{x}$

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