A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.

A. True
B. False

Question

A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.

 		A.	True
 		B.	False

mathmale · Answer

What do YOU think?  What are your reasons for your choice?

anonymous · Answer

its true

anonymous · Answer

@mathmale

mathmale · Answer

What are your reasons for your answer choice?  Perhaps you could answer that by giving an example of long division or synthetic div. where the remainder is zero.

michele_laino · Answer

Hint:
we can apply this theorem about polynomilas:
"GIven the polynomial $P(x)$ and the binomial $x-a$, then we can find two other polynomials $q(x)$ and $r(x)$, such that, the subsequent condition holds:"
$$P\left( x \right) = q\left( x \right)\left( {x - a} \right) + r\left( x \right)$$
where degree of q(x) is less than degree of P(x)

michele_laino · Answer

oops... about polynomials*

mathmale · Answer

Yes (Michele).  Referring to that Theorem, what conclusion can we draw if r(x)=0?