Do Now Decide whether x-1 is a factor of f(x) Factor f(x) into linear factors given that 2 is a zero of f(x) What is the relationship between zeroes and.

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Presentation transcript:

Do Now Decide whether x-1 is a factor of f(x) Factor f(x) into linear factors given that 2 is a zero of f(x) What is the relationship between zeroes and factors?

Use rational zeroes theorem to compile a list of all possible rational zeroes Combine rational zeroes theorem with remainder theorem to test which possibilities are actual solutions

This week is the beef We are adding beefy theorems this week that require us to know how to use remainder theorem as a tool to test for zeroes Must know relationship between factors and theorems

Rational Zeros Theorem Gives us a method to determine all possible candidates for rational zeros of a polynomial function If is a rational number written in lowest terms, and if it is a zero of f, then p is a factor of the constant term and q is a factor of the leading coefficient Key points: p/q in lowest terms p is factor of the constant q is factor of the leading coefficient

RZT- compiling the list Use RZT to compile a list of all possible rational zeroes of the following functions:

RZT- what to do with the list? We have compiled the list of all possible zeros. Now what should we do with it? What should we use it for? Turn and talk to your neighbor and discuss some possible uses of this list; I will randomly call on a few people to share

RZT- why? RZT compiles the list of all possibilities Synthetic division/ remainder theorem narrows down which ones are true Last week: Test to see if a given value is a zero This week: Test to see if a possible value is a zero

RZT- ex #1 List all possible rational zeros of List all p’s: List all q’s: All possible combinations (without repeats) of p/q in lowest terms: Find all rational zeros and FACTOR f(x) into linear factors. Use remainder theorem, looking for R=0

RZT- ex #2 List all possible rational zeros of List all p’s: List all q’s: All possible combinations (without repeats) of p/q in lowest terms: Find all rational zeros and FACTOR f(x) into linear factors. Use remainder theorem, looking for R=0

RZT Summary Use RZT to compile a list of all possibilities Use Remainder Theorem (with synthetic division) to test possibilities Seems long… how do we know when to stop? Number of Zeros Theorem: A function defined by a polynomial of degree n has at most n distinct zeros Has as many zeros as its highest exponent

Class work- due at end of hour Page 338, section 3.3 #35-41 odd (4 problems) Quiz at beginning of hour tomorrow: one rational zeros theorem question asking you to fully factor a polynomial

3.3 Continue Homework We have not finished the section yet #8-60, multiples of 4 Today’s material: 36 & 40 even