Please answer this with steps and for number 1 Give reason for each option
Answers
Answer:
Q-2
(i) degree of the polynomial is 7
(ii) 15
(iii) 3
(iv) 0
Step-by-step explanation:
Solutions :-
Q-1:-
i) Given algebraic expression is 3x²-5x
It is a Polynomial .
Reason :
The algebraic expression has positive powers of the variables
ii) Given algebraic expression is x+1/x
It is not a polynomial.
Reason :
The algebraic expression has negative power of the variable.
The variable x is in the denominator.
iii)Given algebraic expression is √y-8
It is not a polynomial.
Reason :
The algebraic expression has rational power of the variable.
The variable y is under square root
iii)Given algebraic expression is
z⁵-³√z +8
It is not a polynomial.
Reason :
The algebraic expression has rational power of the variable.
The variable z is under cube root .
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Q-2:-
I) Given polynomial is 5x -6x³+8x⁷+6¹x²
On writing it in the standard form:8x⁷-6x³+6x²+5x
Heighest power of all powers of the variables = 7
Degree of the Polynomial = 7
ii) Given polynomial is 2y¹²+3y¹⁰-y¹⁵+y+3
On writing it in the standard form:
-y¹⁵ +2y¹² +3y¹⁰ +y+3
Heighest power of all powers of the variables = 15
Degree of the Polynomial = 15
iii) Given polynomial is (2x³+4x²-2x)/x
=> x(2x²+4x-2)/x
=> 2x²+4x-2
On writing it in the standard form:2x²+4x-2
Heighest power of all powers of the variables = 2
Degree of the Polynomial = 2
iv) Given polynomial is 12
It can be written as 12×x⁰
Heighest power of all powers of the variables = 0
Degree of the Polynomial = 0
Used ormulae:-
Polynomial :-
An algebraic expression has non negative integral powers of the variables present in the given expresion is called a Polynomial.
Degree of the polynomial :-
The heighest of all powers of the all variables in the given polynomial is the degree of the polynomial.
Points to know :-
If any algebraic expression is said to be a polynomial ,
- The variable in the given expresion is not in the denominator .
- It is not under root
- It has not negative power