Remainder and factor theorems
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The document discusses the relationship between the remainder when dividing a function f(x) by (x-c) and the value of f(c). Specifically, it states that the remainder is equal to the value of f(c), and if the remainder is 0, then (x-c) is a factor of the function. This relationship means that using synthetic division to find the remainder can simplify calculations, as the remainder directly provides the value of the function at that point. The document also includes a lame joke about French fries.
Remainder and factor theorems
- 1. Pre-Calculus Warm up 1. Use synthetic division to divide f(x) by 2. What is the remainder? 3. Find the value of 4. What is the relationship between the remainder and the value of the function? 1828472)( 234 xxxxxfLet 2 1 x 2 1 f
- 2. The Remainder and Factor Theorems The Remainder Theorem If f (x) is divided by (x – c) , then the remainder is equal to f (c ). What it means: The remainder in synthetic division is the SAME value as plugging it into the function. This can greatly simplify our calculations!
- 4. The Remainder and Factor Theorems The Factor Theorem If f (x) is divided by (x – c) , and the remainder = 0, then (x – c) is a factor. From the Remainder Theorem: If f (c) = 0 , then (x – c ) is a factor.
- 5. The Lame Joke of the day.. What did the fast French fry say to the slow French fry? And now it’s time for.. Catch Up!