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Home Q & A Board Science-Related Homework Help Mathematics
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LetEnglandShake LetEnglandShake
wrote...
11 years ago
Is a binomial a factor of a polynomial if it leaves a remainder when divided?
Thanks! you saved my ass, your Mcawesome!
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wrote...
#1
11 years ago
no
wrote...
#2
11 years ago
is 7 a factor of 31 if it leaves a remainder when divided?

the answer to both questions is,
no
wrote...
#3
11 years ago
No.   A binomial factor of a polynomial is similar to a factor of a whole number.  It must divide the polynomial evenly.  

e.g.,  x + 1 is a factor of x*2 + 3x + 2 = (x + 2)(x + 1) but not of
x^2 + 4x + 4 = (x + 2)^2.   If you divide it into the latter one, there will be a remainder.
wrote...
#4
11 years ago
No, but the definition of factor:

a is a factor of b if b/a leaves no remainder.
ijmorale Author
wrote...
#5
11 years ago
In many books, this is called "The remainder Theorem"... it goes like this:

If a polynomial p(x) is divided by (x-r) then the remainder will be p(r).

Since you claim that "there is a remainder" you really mean that the remainder is non-zero.  Having p(r) not equal to zero means that p(x) cannot be rewriten as (x-r)q(x) for any polynomial q.
wrote...
#6
11 years ago
No.
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