When #3x^2+6x-10# is divided by x+k, the remainder is 14. How do you determine the value of k?

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Answer 1 · 2017-02-19T07:29:07

The values of #k# are #{-4,2}#

We apply the remainder theorem

When a polynomial #f(x)# is divided by #(x-c)#, we get

#f(x)=(x-c)q(x)+r(x)#

When #x=c#

#f(c)=0+r#

Here,

#f(x)=3x^2+6x-10#

#f(k)=3k^2+6k-10#

which is also equal to #14#

therefore,

#3k^2+6k-10=14#

#3k^2+6k-24=0#

We solve this quadratic equation for #k#

#3(k^2+2k-8)=0#

#3(k+4)(k-2)=0#

So,

#k=-4#

or

#k=2#