Question 1188350
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Given f(x)=x^3+kx+2, and x+1 is a factor of f(x), then what is the value of k?
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<pre>
The fact that (x+1) is a factor of the polynomial f(x) = x^3 + kx + 2, means that the value of -1
is the root of this polynomial: f(-1) = 0,  due to the Remainder theorem.


So, we substitute x= -1 into the polynomial and equate it to zero


    (-1)^3 + k*(-1) + 2 = 0.


It is an equation to determine the value of k.  So, simplify and find k


    -1 -k + 2 = 0

    -1 + 2 = k

     k = 1.


<U>ANSWER</U>.  k = 1.
</pre>

Solved.


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If you want to see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Finding-unknown-coefficients-of-a-polynomial-having-given-some-info-about-its-polyn-divis.lesson>Finding unknown coefficients of a polynomial having given info about its polynomial divisors</A>

in this site.


On the Remainder theorem, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial (x-a) and the Remainder theorem</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Solved-problems-on-the-Remainder-theorem.lesson>Typical problems on the Remainder theorem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Advanced-problems-on-the-Remainder-theorem.lesson>Advanced problems on the Remainder theorem</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Finding-unknown-coefficients-of-a-polynomial-having-given-some-info-about-its-polyn-divis.lesson>Finding unknown coefficients of a polynomial having given info about its polynomial divisors</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Finding-unknown-coefficients-of-a-polynomial-based-on-some--given-info-about-its-routes.lesson>Finding unknown coefficients of a polynomial based on some given info about its roots</A> 

in this site.