OBJECTIVE: I will be able to calculate the real zeros of a polynomial function using synthetic division and the Rational Zero Theorem through use of in-class.

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Presentation transcript:

OBJECTIVE: I will be able to calculate the real zeros of a polynomial function using synthetic division and the Rational Zero Theorem through use of in-class notes and activities.

 Remainder Theorem: ◦ The remainder of f(x)/(x-c) = f(c)  Factor Theorem: ◦ If f(c) = 0, then (x-c) is a factor of f(x) ◦ Converse: If (x-c) is a factor of f(x), then f(c) = 0

1. The factor theorem says that finding roots of a polynomial is a the same as finding factors and vice-versa 2. If ‘c’ is a real root, then (x-c) is a factor & graph crosses x-axis at x=c 3. If ‘c’ is a double root, then (x-c) 2 is a factor and it touches the graph at x=c 4. In Real Numbers, complex roots are not allowed are excluded from root counts

List all possible rational roots is P/Q where P is the constant and Q is the leading coefficient Lists possible roots! Not all possible roots are actually roots