Classify the following polynomials as polynomials in one-variable, two variables etc.:

(i) x² − xy + 7y²

(ii) x² − 2tx + 7t² − x + t

(iii) t³ − 3t² + 4t − 5

(iv) xy + yz + zx

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Solution

(i)

Here, x and y are two variables.

So, it is polynomial in two variables.

(ii)

Here, x and t are two variables.

So, it is polynomial in two variables.

(iii)

Here, only t is variable.

So, it is polynomial in one variable.

(iv)

Here, x, y and z are three variables

So, it is polynomial in three variables.

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Classify the following polynomials as polynomials in one-variable, two variables etc.: (i) x2 − xy + 7y2 (ii) x2 − 2tx + 7t2 − x + t (iii) t3 − 3t2 + 4t − 5 (iv) xy + yz + zx

Classify the following polynomials as polynomials in one-variable, two variables etc.:

(i) x² − xy + 7y²

(ii) x² − 2tx + 7t² − x + t

(iii) t³ − 3t² + 4t − 5

(iv) xy + yz + zx