1. Expain polynomials in one variable with suitable 2 examples . each example should be proper explaination .
2. Explain zeros of polynomial with suitable 2 examples . each example should be proper explaination .
3. Explain Reminder theorm with suitable 2 examples . each example should be proper explaination .
4. Explain factorization of polynomials with suitable 2 examples . each example should be proper explaination .
Explain clearly with 2 examples with good explaination.
Note : Don't spam , Don't copy .
Answers
Step-by-step explanation:
1) Polynomial in one variable:-
An algebraic expression having non negative integral powers of variables present in the given expression is called a polynomial.
If a polynomial having only one variable is called a polynomial in one variable .
Ex : 2x+3 ; 3x^2+5x-6;6x^3+7x^2+8x+9...
2)Zeroes of a polynomial:-
A value of variables satisfying the given Polynomial are called zeroes of the given polynomial.
Ex:-
3 is the zero of x-3.
Since when we substitute 3 in X we get zero
2,1 are the zeroes of x^2-3x+2
If x= 2 then (2)^2-3(2)+2=4-6+2=6-6=0
If x=1 then (1)^2-3(1)+2=1-3+2=3-3=0
3) Remainder Theorem:-
A polynomial p(x) of the degree greater than or equal to one and (x-a) is any linear polynomial then if(x-a) is divided by p(x) then the remainder is p(a).
Ex:-
P(x)=4x^2-2x+1 is divided by (x-1) then the remainder is 3
P(1)=4(1)^2-2(1)+1=4-2+1=3
P(x)=x^2-9 is divided by (x-3) then the remainder is 0
P(3)=3^2-9=9-9=0
4) Factorization:-
Expressing the given Polynomial into product of factors is called its factorization.
Ex:-
x^2-6x+9
=>x^2-3x-3x+9
=>x(x-3)-3(x-3)
=>(x-3)(x-3)
and
x^2-9
=>x^2-3^2
=>(x+3)(x-3)
Since (a+b)(a-b)=a^2-b^2