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1. x – r is a factor of P(x) if and only if the remainder R of P(x) =_______. 2. By the Remainder Theorem, P(r) = _______. 3. If the remainder P( r) = 0, then _______ is a factor of P( x ). 4. The remainder in P(x) ≠ 0, we can say that ( x - r) is _______ of P(x).

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Answer:

1. x-r is a factor of P(x) if and only if the remainder R of P(x) is divided by (x-r) is equals to 0.

2. By the remainder theorem, R=0 if and only if (x-r) is a factor of P(x).

3. Thus, (x-3) is a factor of P(x) if and only if P(r)=0