Use synthetic division and the given factor to completely factor then polynomial function.

Given:
[tex]x^3+9x+14x-24;x+6[/tex]Find-: Factor
Sol:
[tex]\frac{x^3+9x+14x-24}{x+6}[/tex]Eq become.
[tex]=(x+6)(x^2+3x-4)[/tex]Factor is:
[tex]x^2+3x-4[/tex][tex]\begin{gathered} =x^2+3x-4 \\ \\ =x^2+4x-x-4 \\ \\ =x(x+4)-1(x+4) \\ \\ =(x+4)(x-1) \end{gathered}[/tex]