Question

which of the following is a binomial of degree 20 ?​

Answer 1

SOLUTION

COMPLETE QUESTION

Which of the following is a binomial of degree 20

$\displaystyle \sf{1. \: \: 20x + 1 }$

$\displaystyle \sf{2. \: \: \frac{x}{20} + 1}$

$\displaystyle \sf{3. \: \: {x}^{20} + 1}$

$\displaystyle \sf{4. \: \: {x}^{2} + 1}$

EVALUATION

CHECKING FOR OPTION : 1

Here the given polynomial is 20x + 1

Highest power of its variable that appears with nonzero coefficient is 1

Hence the polynomial has degree 1

So the option is not correct

CHECKING FOR OPTION : 2

Here the given polynomial is

$\displaystyle \sf{ \frac{x}{20} + 1}$

Highest power of its variable that appears with nonzero coefficient is 1

Hence the polynomial has degree 1

So the option is not correct

CHECKING FOR OPTION : 3

Here the given polynomial is

$\displaystyle \sf{ {x}^{20} + 1 }$

Highest power of its variable that appears with nonzero coefficient is 20

Hence the polynomial has degree 20

So the option is correct

CHECKING FOR OPTION : 4

Here the given polynomial is

$\displaystyle \sf{ {x}^{2} + 1 }$

Highest power its variable that appears with nonzero coefficient is 2

Hence the polynomial has degree 2

So the option is not correct

FINAL ANSWER

Hence the correct option is

$\displaystyle \bf{3. \: \: {x}^{20} + 1}$

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