unit 2, lesson 4 theorems about zeros. getting started find the quotient and remainder when is...

UNIT 2, LESSON 4

THEOREMS ABOUT ZEROS

GETTING STARTED

• Find the quotient and remainder when

is divided by x-3.

542 23 xxxxf

GETTING STARTED

• Find the quotient and remainder when

is divided by x-3. 542 23 xxxxf

212 Rxx

GETTING STARTED

• Find the quotient and remainder when

is divided by x-3.

• Find f(3).

542 23 xxxxf

212 Rxx

GETTING STARTED

• Find the quotient and remainder when

is divided by x-3.

• Find f(3).

542 23 xxxxf

212 Rxx

2

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.

53 2479 xxxf

APPLICATION

•Find the remainder when

is divided by x-1.

53 2479 xxxf

9

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

324 23 xxxxf

PUTTING IT ALL TOGETHER…

•Determine if x-3 is a factor of

324 23 xxxxf

03323433 23 f

PUTTING IT ALL TOGETHER…

•Determine if x-3 is a factor of

324 23 xxxxf

03323433 23 f