UNIT 2, LESSON 4 THEOREMS ABOUT ZEROS. GETTING STARTED Find the quotient and remainder when is divided by x-3.

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Presentation transcript:

UNIT 2, LESSON 4 THEOREMS ABOUT ZEROS

GETTING STARTED Find the quotient and remainder when is divided by x-3.

GETTING STARTED Find the quotient and remainder when is divided by x-3.

GETTING STARTED Find the quotient and remainder when is divided by x-3. Find f(3).

GETTING STARTED Find the quotient and remainder when is divided by x-3. Find f(3).

REMAINDER THEOREM If a polynomial f(x) is divided by x-c, then the remainder is the number f(c).

APPLICATION Find the remainder when is divided by x-1.

APPLICATION Find the remainder when is divided by x-1.

QUERY… What good does being able to quickly calculate the remainder do for us?

FACTOR THEOREM The number c is a root of the polynomial f(x) exactly when x-c is a factor of f(x).

PUTTING IT ALL TOGETHER… Determine if x-3 is a factor of

PUTTING IT ALL TOGETHER… Determine if x-3 is a factor of

PUTTING IT ALL TOGETHER… Determine if x-3 is a factor of