Difference between revisions of "Remainder Theorem"

(Example 1)
m (Removed redirect to Polynomial remainder theorem)
(Tag: Removed redirect)
 
(11 intermediate revisions by 4 users not shown)
Line 1: Line 1:
=Theorem=
+
'''Remainder Theorem''' may refer to:
The Remainder Theorem states that the remainder when the polynomial <math>P(x)</math> is divided by <math>x-a</math> (usually with synthetic division) is equal to the simplified value of <math>P(a)</math>.
+
*[[Polynomial Remainder Theorem]]
 
+
*[[Chinese Remainder Theorem]]
=Examples=
 
==Example 1==
 
What is the remainder when <math>x^2+2x+3</math> is divided by <math>x+1</math>?
 
 
 
==Solution==
 
Using synthetic or long division we obtain the quotient <math>1+\frac{2}{x^2+2x+3}</math>. In this case the remainder is <math>2</math>. However, we could've figured that out by evaluating <math>P(-1)</math>. Remember, we want the divisor in the form of <math>x-a</math>. <math>x+1=x-(-1)</math> so <math>a=-1</math>.
 
 
 
<math>P(-1) = (-1)^2+2(-1)+3 = 1-2+3 = \boxed{2}</math>
 
 
 
{{stub}}
 
hello
 

Latest revision as of 15:42, 27 February 2022