Question

Verify whether following algebraic expressions are polynomial or not.
(1) p(x) = x⁷ + 10x⁵ + 4x³ + 3x + I
(2) p(x) = x⁻⁵/² + 10x + 4x
(3) p(x) = x + 1/x

Answer 1

Answer:

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Answer 2

Answer:

1) it is a Polynomial

2) it is not a Polynomial

3) it is not a Polynomial

Step-by-step explanation:

In this question

We need to find which of the following is a Polynomial

POLYNOMIAL - A Mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by atleast one variables raised to a non-negative integral power (such as $a\ +\ bx\ +\ cx^{2}$)

1) p(x) = $x^{7}\ +\ 10x^{5}\ +\ 4x^{3}\ +\ 3x\ +\ 1$

It is a polynomial as x(variable) has a non-negative  integral power.

2) p(x) = $x^{\frac{-5}{2}}\ +\ 10x\ +\ 4x$

It is not a polynomial as x(variable) has a negative integral power.

3) p(x) = $x\ +\ \frac{1}{x}$

It is not a polynomial as x(variable) has a negative integral power.