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