Real Zeros Intro - Chapter 4.2.

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Presentation transcript:

Real Zeros Intro - Chapter 4.2

Rational Zeros The Rational Root Theorem Let P be a polynomial function with integer coefficients in standard form. If _______ (a reduced fraction ) is a _______ of then ROOT p is a factor of the ______________ term of P. CONSTANT q is a factor of the ________________________ of P LEADING COEFFICIENT

Completely Factored Polynomials Example 4: Factor f(x) completely. Step 1: List all ____________ rational roots. POSSIBLE Step 2: ________and choose the best rational root from your list. GRAPH Looks like -3 or 1/2

Step 3: Use _____________ division to find all _____________ factors. SYNTHETIC RATIONAL

Step 4: Find all ________________ zeros using the _________________________ IRRATIONAL QUADRATIC EQUATION Step 5: Write in _____________ form. FACTORED

Example 1: List all of the possible rational roots of q = ____ Factors of p = _________________ Factors of q = _________________ All possible rational roots of f(x) are