Please help with #33 and #37
2 answers:
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Answer:
SUMMARY:
→ Not a Polynomial
→ A Polynomial
→ A Polynomial
→ Not a Polynomial
→ A Polynomial
→ Not a Polynomial
Step-by-step explanation:
The algebraic expressions are said to be the polynomials in one variable which consist of terms in the form .
Here:
= non-negative integer
= is a real number (also the the coefficient of the term).
Lets check whether the Algebraic Expression are polynomials or not.
Given the expression
If an algebraic expression contains a radical in it then it isn’t a polynomial. In the given algebraic expression contains , so it is not a polynomial.
Also it contains the term which can be written as
, meaning this algebraic expression really has a negative exponent in it which is not allowed. Therefore, the expression
is not a polynomial.
Given the expression
This algebraic expression is a polynomial. The degree of a polynomial in one variable is considered to be the largest power in the polynomial. Therefore, the algebraic expression is a polynomial is a polynomial with degree 5.
Given the expression
in a polynomial with a degree 4. Notice, the coefficient of the term can be in radical. No issue!
Given the expression
is not a polynomial because algebraic expression contains a radical in it.
Given the expression
a polynomial with a degree 3. As it does not violate any condition as mentioned above.
Given the expression
Therefore, is not a polynomial because algebraic expression really has a negative exponent in it which is not allowed.
SUMMARY:
→ Not a Polynomial
→ A Polynomial
→ A Polynomial
→ Not a Polynomial
→ A Polynomial
→ Not a Polynomial