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If you divide a polynomial by a binomial, how do you know if the binomial is a factor...

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ktchiate | (Level 1) Honors

Posted December 31, 2012 at 1:21 AM via web

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If you divide a polynomial by a binomial, how do you know if the binomial is a factor of the polynomial?

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted December 31, 2012 at 1:54 AM (Answer #1)

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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.`



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