SOLUTION: In questions 1 - 5, decide whether the given expression is a polynomial and tell why or why not. 1. 3x^2 - 5x + 2 AThis is not a polynomial because 5x is subtracted fr

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Question 1153849: In questions 1 - 5, decide whether the given expression is a polynomial and tell why or why not.

1. 3x^2 - 5x + 2
AThis is not a polynomial because 5x is subtracted from 3x2.
BThis is a polynomial because 5 is in front of x.
CThis is not a polynomial because 3 is in front of x2.
DThis is a polynomial because it is the sum of monomials with whole-number exponents.
E This is not a polynomial because it contains x2.
F Not enough information.

2. 1/x^4 + 5x^2 - 4x + 1
AThis is a polynomial because it contains x2
BThis is not a polynomial because x4 is in the denominator.
CThis is not a polynomial because it contains x2
DThis is not a polynomial because there are too many exponents.
E This is a polynomial because the exponents can be divided evenly by two.
F Not enough information.

3. 4x^-3 + 3x^2 + 2x + 1
AThis is not a polynomial because there are too many exponents.
BThis is a polynomial because it contains x2
CThis is not a polynomial because it contains x2
DThis is not a polynomial because 3 is in front of x2
E This is not a polynomial because the terms are not written in the correct order.
F This is not a polynomial because x is raised to a negative power in the first term.

4. 7x^5 + 3x^4 - 2x^2 + 7
ANot enough information.
BThis is not a polynomial because 3 is in front of x2
CThis is a polynomial because it contains x2
DThis is not a polynomial because 3 is in front of x4
E This is a polynomial because it is the sum of monomials with whole-number exponents.
F This is not a polynomial because the exponents are not divisible by 2.

5. (√x) + 12
AThis is not a polynomial because the variable is underneath a square root sign.
BThis is not a polynomial because it does not contain x2
CThis is not a polynomial because the exponents are not divisible by 2.
DThis is a polynomial because it contains no negative exponents.
E This is a polynomial because there are no variables in the denominator.
F This is not a polynomial because the x has no positive coefficient.
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13198) (Show Source):
You can put this solution on YOUR website!

The definition of a polynomial requires that every power of x be a whole number -- no fractional or negative exponents.

Note that can be seen in answer choice E for problem 4.

Note that roots are fractional exponents....

Answer each one yourself based on that requirement.

Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!

In particular, for an expression to be a polynomial term, it must contain
- square roots of variables,
- fractional or negative powers on the variables, and
- variables in the denominators of any fractions.

1.
D This is a polynomial because it is the sum of monomials with whole-number exponents.

2.
B This is not a polynomial because is in the denominator.

3.
F This is not a polynomial because x is raised to a negative power in the first term.

4.
E This is a polynomial because it is the sum of monomials with whole-number exponents.

5.
A This is not a polynomial because the variable is underneath a square root sign.