Let us consider f(x) =
![\[\left( \mathbf{3k}\text{ }+\text{ }\mathbf{2} \right){{\mathbf{x}}^{\mathbf{3}}}~+\text{ }\left( \mathbf{k}\text{ }\text{ }\mathbf{1} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-206ee1d6f9a8fabfa9d0896d1a0db0ef_l3.png "Rendered by QuickLaTeX.com")
Now,
![\[2x\text{ }+\text{ }1\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2694fca8de1444d16dfc03ce0670e49f_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }=\text{ }-1/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-03b20f4523af69b5aa2c5996ca535a45_l3.png "Rendered by QuickLaTeX.com")
As,
![\[2x\text{ }+\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-575ddc6b0d6cbae74b920ec54273b233_l3.png "Rendered by QuickLaTeX.com")
is a factor of f(x) then the remainder should be
![\[0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b4f4fbf425b3e7b1e844d7922169d13c_l3.png "Rendered by QuickLaTeX.com")
.
![\[f\left( -1/2 \right)\text{ }=\text{ }\left( 3k\text{ }+\text{ }2 \right){{\left( -1/2 \right)}^{3}}~+\text{ }\left( k\text{ }\text{ }1 \right)\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-016929526f582ad4033ed1145bb0b5ff_l3.png "Rendered by QuickLaTeX.com")
![\[\begin{array}{*{35}{l}} 5k\text{ }=\text{ }10\text{ }=\text{ }0 \\ k\text{ }=\text{ }2 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-239b25fce56b3b72b04994f84385c614_l3.png "Rendered by QuickLaTeX.com")
Find the value of k, if
![\[\mathbf{2x}\text{ }+\text{ }\mathbf{1}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-16fd72fb9940c8b247bd1589bb6b4d2a_l3.png "Rendered by QuickLaTeX.com")
Let us consider f(x) =
Now,
As,
is a factor of f(x) then the remainder should be
.
