SOLUTION: if x+1 is a factor of x^3+3x^2+kx+4, find the value of k.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: if x+1 is a factor of x^3+3x^2+kx+4, find the value of k.      Log On


   



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) About Me  (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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graph%28300%2C200%2C-10%2C10%2C-10%2C10%2Cx%5E3%2B3x%5E2%2B6x%2B4%29

Answer by ikleyn(52782) About Me  (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.
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If  x+1  is a factor of  x%5E3%2B3x%5E2%2Bkx%2B4,  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:

%28-1%29%5E3+%2B+3%28-1%29%5E2+%2B+k%2A%28-1%29+%2B+4 = 0,     or

-1 + 3 - k + 4 = 0.

It is the equation to determine  k,  and it gives

k = -1 + 3 + 4 = 6.