How do you determine the value of k if the remainder is 3 given #(kx^3+3x+1) div(x+2)#?

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Answer 1 · 2017-07-27T06:26:52

#k=-1#

The Remainder Theorem states that:

if the polynomial #P(x)" " #is divided by#" "(x-a)" "#the remainder is #P(a)#

In this case we have

#P(x)=kx^3+3x+1#

and the divisor #(x+2)=>a=-2#

#:.P(-2) = 3#

#:.P(-2)=k(-2)^3+3xx -2+1=3#

#=>-8k-6+1=3#

#-8k-5=3#

#-8k=8#

#=>k=-1#