How do you find the value of #k# in #(x^3+kx^2-9) -: (x+2)# so the remainder is 7?

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Answer 1 · 2018-01-19T17:04:27

#k=-12#

we use the remainder theorem for this

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

we can rewrite this division as follows

#(x^3+kx-9)=Q(x)(x+2)+7#

substitute #x=-2#

#(-2)^3+k(-2)-9=cancel(Q(-2)(-2+2))+7#

#:.-8-2k-9=7#

#2k=-24#

#k=-12#