SOLUTION: if x+1 is a factor of x^3+3x^2+kx+4, find the value of k.
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Question 995921: if x+1 is a factor of x^3+3x^2+kx+4, find the value of k.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
-1/1---3---k---4
---1;;;-1;;;-2;;;-k+2
==========
;;;;;;;;;;2 ;;k-2
=============
;;;;;;;;;;;;;;;;;;;-k+2
4+-k+2=0
-k= -6
k=6
==========
check
the function should be x^3+3x^2+6x+4
the factors should be (x+1), given, and x^2+2x+4
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Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
.
if x+1 is a factor of x^3+3x^2+kx+4, find the value of k.
-----------------------------------------------------------
If x+1 is a factor of , then x = -1 is the root of this polynomial.
It means that if we substitute -1 instead of x into the polynomial, we get 0:
= , or
-1 + 3 - k + 4 = 0.
It is the equation to determine k, and it gives
k = -1 + 3 + 4 = 6.
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