Answer:
k = 10
Explanation:
The initial polynomial is:
[tex]f(x)=3x^3+13x^2+19x+k[/tex]If f(-2) = 0, then when we replace x by -2, the result will be 0. It means that we can write the following equation:
[tex]\begin{gathered} f(-2)=3(-2)^3+13(-2)^2+19(-2)+k=0 \\ 3(-2)^3+13(-2)^2+19(-2)+k=0 \end{gathered}[/tex]Therefore, we can solve for k as follows:
[tex]\begin{gathered} 3(-8)+13(4)+19(-2)+k=0 \\ -24+52-38+k=0 \\ -10+k=0 \\ -10+k+10=0+10 \\ k=10 \end{gathered}[/tex]So, the value of k is 10
