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Which of the following expression are polynomials in one variable and which are non? Give reasons for your answer.

(i) 3x

2

−2x+5

(ii) x

2

+

2

(iii) p

2

−3p+q

(iv) y+

y

2

(v) 5

x

+x

5

(vi) x

100

+y

100

Medium

Solution

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(i)3x

2

−2x+5 Polynomial is one variable

Here x is the only variable.

(ii)x

2

+

2

Polynomial is one variable

Here x is the only variable.

(iii)p

2

−3p+q Polynomial with two variables.

Here p&q are variables.

(iv)y+

y

2

Not a polynomial

∵y is having −ve power in second term.

(v)5

x

+x

5

Not a polynomial

∵x is having fractional power in first term.

(vi)x

100

+y

100

Polynomial with two variables.

Here x&y are variables.

300

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