How many different arrangements of the letters in the word power
1 answer:
5 letters ==> 
power powre poewr poerw porwe porew pwoer pwore pweor pwero pwroe pwreo peowr peorw pewor pewro perow perwo prowe proew prwoe prweo preow prewo opwer opwre opewr operw oprwe oprew owper owpre owepr owerp owrpe owrep oepwr oeprw oewpr oewrp oerpw oerwp orpwe orpew orwpe orwep orepw orewp wpoer wpore wpeor wpero wproe wpreo woper wopre woepr woerp worpe worep wepor wepro weopr weorp werpo werop wrpoe wrpeo wrope wroep wrepo wreop epowr eporw epwor epwro eprow eprwo eopwr eoprw eowpr eowrp eorpw eorwp ewpor ewpro ewopr eworp ewrpo ewrop erpow erpwo eropw erowp erwpo erwop rpowe rpoew rpwoe rpweo rpeow rpewo ropwe ropew rowpe rowep roepw roewp rwpoe rwpeo rwope rwoep rwepo rweop repow repwo reopw reowp rewpo rewop
power powre poewr poerw porwe porew pwoer pwore pweor pwero pwroe pwreo peowr peorw pewor pewro perow perwo prowe proew prwoe prweo preow prewo opwer opwre opewr operw oprwe oprew owper owpre owepr owerp owrpe owrep oepwr oeprw oewpr oewrp oerpw oerwp orpwe orpew orwpe orwep orepw orewp wpoer wpore wpeor wpero wproe wpreo woper wopre woepr woerp worpe worep wepor wepro weopr weorp werpo werop wrpoe wrpeo wrope wroep wrepo wreop epowr eporw epwor epwro eprow eprwo eopwr eoprw eowpr eowrp eorpw eorwp ewpor ewpro ewopr eworp ewrpo ewrop erpow erpwo eropw erowp erwpo erwop rpowe rpoew rpwoe rpweo rpeow rpewo ropwe ropew rowpe rowep roepw roewp rwpoe rwpeo rwope rwoep rwepo rweop repow repwo reopw reowp rewpo rewop
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<h3>Answer: 25</h3>
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Explanation:
Check out the image below. I've posted the synthetic division table. The value at the very end of the bottom row is the remainder. By the remainder theorem, this is exactly the value of g(-5).
Recall the remainder theorem says: If you divide p(x) by (x-k), then the remainder is p(k). In this case, k = -5 is our test root which is the value placed in the box on the left.
As a way to check the answer, we can say
g(x) = 2x^2 + 6x + 5
g(-5) = 2(-5)^2 + 6(-5) + 5
g(-5) = 25
So the answer is confirmed.