If you divide a polynomial by a binomial, how do you know if the binomial is a factor of the polynomial?
In mathematics, a polynomial is an expression of finite length constructed from variables (also called indeterminate) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The polynomial with two terms is called a binomial.
For example `x^3+2x+2` is a polynomial and `x+2` is a binomial.
We can use the remainder theorem to find out whether a binomial is a factor of a polynomial.
In remainder therem it states that a polynomial f(x) is divided by (x-a) which is a binomial the remainder is given by f(a).
So when it comes to a factor f(a) = 0
Now the problem is clear.
You can substitute the value of binomial (which binomial equate to 0) to the polynomial and check whether the remainder is 0.If so it is a factor otherwise not.
Just see the example for more.....
polynomial `f(x) = x^2+2x+1`
Binomial `= (x+1)`
`(x+1) = 0` when `x = -1`
`f(-1) = (-1)^2+2(-1)+1 = 0`
So `(x+1)` is a factor of `x^2+2x+1.`