which of the following expression are polynomials
(x-1) (x+1)
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Asked on January 17, 2020 by
Pawan Shekhawat
Which of the following expressions is a polynomial ?
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ANSWER
We know that a polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power (usually positive whole number) and multiplied by a coefficient.
The simplest polynomials have one variable.
A one-variable polynomial of degree n has the following form:
a
n
x
n
+a
n−1
x
n−1
+...+a
2
x
2
+a
1
x
1
+a
where, the a's represent the coefficients and x represents the variable.
Now, consider the given options:
(a) x+
x
1
can be rewritten as x+x
−1
, which is not a polynomial because the exponent of the variable x is −1 which is a negative number.
(b)
x
+x+x
2
can be rewritten as x
2
1
+x+x
2
, which is not a polynomial because the exponent of the variable x is
2
1
, which is not a whole number.
(c)
2
x+x
3
+3x
2
is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a power and multiplied by a coefficient. Also, the exponent of the variable x is a whole number.
Therefore,
2
x+x
3
+3x
2
is a polynomial.
(d) x
2
+x
−2
+2 which is not a polynomial because the exponent of the variable x is −2, which is a negative number.
Hence, the expression
2
x+x
3
+3x
2
is not a polynomial. plzzz follow me