Question

when f(y)=y^4-4y^3+8y^2-my+n is divided by y+1 and y-1, we get the remainder 10 and 16 respectively.Find the remainder when f(y) is divided by y-3.

Answer 1

ANSWER.....




A polynomial expression S(x) in one variable x is an algebraic expression in x term as
S(x)=anxn+a(n-1)x(n-1)+a(n-2)x(n-2)+.....+ax+a0
Where an,an-1,....,a,a0 are constant and real numbers and an is not equal to zero

Some important points to remember
1) an,an-1,...,a,a0 are called the coefficients for xn,xn-1 ,..,x,x0
2) n is called the degree of the polynomial
3) when an,an-1,....,a,a0 it is called zero polynomial
4) A constant polynomial is the polynomial with zero degree, it is a constant value polynomial
5) A polynomial of one item is called monomial, two items binomial and three items as trinomial
6) A polynomial of one degree is called linear polynomial, two degree as quadratic polynomial and degree three as cubic polynomial


Value of the polynomial:


Lets take a example of polynomial
S(x) =x2 +1
Then 
When we put the value of x=2,then
S(2)=4+1=5
The S(2) is the called the value of polynomial at x=2
In General terms, the value of polynomial at x=a is S(a)