which of following is a term of polynomials
1_ 2x
2_3/x
3_root x
4_root x2
Answers
Step-by-step explanation:
For an expression to be a polynomial term, any variables in the expression must have whole-number powers (or else the "understood" power of 1, as in x1, which is normally written as x). A plain number can also be a polynomial term. In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Here are some examples:
This is NOT a polynomial term...
6x –2
...because the variable has a negative exponent.
This is NOT a polynomial term...
\small{ \dfrac{1}{x^2} }
x
2
1
...because the variable is in the denominator.
This is NOT a polynomial term...
\small{ \sqrt{x\,} }
x
...because the variable is inside a radical.
This IS a polynomial term...
4x2
...because it obeys all the rules.
This is also a polynomial term...
\small{ \dfrac{5^{2/3}}{4} \sqrt{3\,}\, x^{47} }
4
5
2/3
3
x
47
...because the variable itself has a whole-number power.
That last example above emphasizes that it is the variable portion of a term which must have a whole-number power and not be in a denominator or radical. The numerical portions of a term can be as messy as you like. (But, at least in your algebra class, that numerical portion will almost always be an integer..)
Terminology
To create a polynomial, one takes some terms and adds (and subtracts) them together. Here is a typical polynomial: