Polynomial Division and the Remainder Theorem
Master the key concepts of polynomial division, synthetic division, and the Remainder and Factor Theorems.
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Questions Covered in This Set
8 cards to master
What is the Remainder Theorem?
When a polynomial P(x) is divided by (x - c), the remainder is P(c).
What is the Factor Theorem?
(x - c) is a factor of P(x) if and only if P(c) = 0.
When is synthetic division applicable?
When dividing by a linear factor of the form (x - c).
In the division P(x) = D(x) × Q(x) + R, what do Q(x) and R represent?
Q(x) is the quotient polynomial and R is the remainder.
How do you verify if (x - 5) is a factor of P(x)?
Evaluate P(5). If P(5) = 0, then (x - 5) is a factor.
In synthetic division, what does the last number in the bottom row represent?
The remainder of the division.
What is the first step in polynomial long division?
Divide the leading term of the dividend by the leading term of the divisor.
How can you quickly find the remainder when dividing P(x) by (x - 7)?
Evaluate P(7) using the Remainder Theorem.
