Difference between revisions of "Remainder Theorem"

Latest revision as of 15:42, 27 February 2022

Remainder Theorem may refer to:

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-=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 in <math>\frac{x^2+2x+3}{x+1}</math>?
-==Solution==
-Using synthetic or long division we obtain the quotient <math>x+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>x=-1</math>.
-<math>P(-1) = (-1)^2+2(-1)+3 = 1-2+3 = \boxed{2}</math>