Hi,

(x^4+3x^3-4x^2)÷(x+4)

-4	1	3	-4

		-4	4

	1	-1	0

  x^3 - x^2 

Remainder = 0  

(x + 4) a factor

Wish You the Best in your Studies. 

Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
 .





   Theorem   (the remainder theorem)



   1. The remainder of division the polynomial    by the binomial    is equal to the value    of the polynomial. 



   2. The binomial    divides the polynomial    if and only if the value of    is the root of the polynomial  ,  i.e.  .



   3. The binomial    factors the polynomial    if and only if the value of    is the root of the polynomial  ,  i.e.  .







See the lessons



    - Divisibility of polynomial f(x) by binomial x-a and the Remainder theorem



    - Solved problems on the Remainder thoerem



in this site.







Also,  you have this free of charge online textbook in ALGEBRA-II in this site



    ALGEBRA-II - YOUR ONLINE TEXTBOOK.





The referred lessons are the part of this online textbook under the topic 

"Divisibility of polynomial f(x) by binomial (x-a). The Remainder theorem".





Save the link to this online textbook together with its description





Free of charge online textbook in ALGEBRA-I

https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson





to your archive and use it when it is needed.







 

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