The factor theorem (HSC SSCE Mathematics Extension 1): Flashcards
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10 cards from this deck
What does the Factor Theorem state?
What does the Factor Theorem state?
If P(a) = 0, then (x - a) is a factor of P(x).
What is a zero of a polynomial?
What is a zero of a polynomial?
A value of x where P(x) = 0.
How does the Factor Theorem simplify polynomials?
How does the Factor Theorem simplify polynomials?
It helps find factors and zeros easily.
What is the significance of finding zeros?
What is the significance of finding zeros?
It aids in graphing and understanding polynomials.
What is the first step in using the Factor Theorem?
What is the first step in using the Factor Theorem?
Evaluate P(a) at potential rational zeros.
What is a rational zero?
What is a rational zero?
A potential zero derived from constant term factors.
What does polynomial division confirm?
What does polynomial division confirm?
It verifies that a linear term is a factor.
What is the Rational Root Theorem?
What is the Rational Root Theorem?
It lists potential rational zeros based on factors.
How do you find factors of P(x)?
How do you find factors of P(x)?
Test values of x to see if P(x) = 0.
What is P(2) for P(x) = 2x^3 - 3x^2 - 8?
What is P(2) for P(x) = 2x^3 - 3x^2 - 8?
P(2) = -6, so (x - 2) is not a factor.