Which of the following expressions are not polynomials in one variable? (a) 4x²-3x + 7 (b) y² + √2 (c) x + (d) x²+x-6
2 X
Answers
Answer:
(i) In 4x
2
−3x+7. all the indies of x are whole numbers. So, it is a polynomial in one variable x.
(ii) In y
2
+
2
the index of y is a whole number. So, it is a polynomial in one variable y.
(iii) In 3
t
+t
2
=3t
2
1
+
2
t, here the exponent of first term is
2
1
, which is not whole number therefore is it not a polynomial.
(iv) In y+
y
2
=y+2y
−1
, here the exponent of first term is −1, which is not whole number, therefore, is it not a polynomial.
(v) In x
10
+y
3
+t
50
is not a polynomial in one variable as three variable x,y and t occur in it.
We know that a polynomial is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non-negative integral power (whole number).
(i) 3x
3
−2x+1 can be rewritten as:
3x
3
−2x+1x
0
The powers of the variable x in the above equation are 3,1 and 0 which are whole numbers.
Therefore, 3x
3
−2x+1 is a polynomial.
(ii) x
2
+x
x
−2 can be rewritten as:
x
2
+x(x)
2
1
−2x
0
=x
2
+(x)
2
1
+1
−2x
0
=x
2
+(x)
2
3
−2x
0
The powers of the variable x in the above equation are 2,
2
3
and 0, where
2
3
is not a whole number.
Therefore, x
2
+x
x
−2 is not a polynomial.
(iii) x
4
+2x can be rewritten as:
x
4
+2x
1
The powers of the variable x in the above equation are 4 and 1 which are whole numbers.
Therefore, x
4
+2x is a polynomial.
(iv) 4x
2
+3x−5 can be rewritten as:
4x
2
+3x−5x
0
The powers of the variable x in the above equation are 2,1 and 0 which are whole numbers.
Therefore, 4x
2
+3x−5 is a polynomial.
(v)
2x
+
3
can be rewritten as:
(2x)
2
1
+
3
x
0
The powers of the variable x in the above equation are
2
1
and 0, where
2
1
is not a whole number.
Therefore,
2x
+
3
is not a polynomial.