First find Divisor
[tex]\\ \sf\longmapsto x^2-(-3-2)+(-3)(-2)[/tex]
[tex]\\ \sf\longmapsto x^2+5x+6[/tex]
Dividend given by
[tex]\\ \sf\longmapsto x^4-x^3-16x^2+4x+48[/tex]
We know
[tex]\boxed{\sf Dividend=Divisor\times Quotient +Remainder}[/tex]
[tex]\\ \sf\longmapsto Dividend=Divisor\times Quotient[/tex]
[tex]\\ \sf\longmapsto Quotient=\dfrac{Dividend}{Divisor}[/tex]
[tex]\\ \sf\longmapsto \dfrac{x^4-x^3-16x^2+4x+48}{x^2+5x+6}[/tex]
[tex]\\ \sf\longmapsto x^2-6x+8[/tex]
Now factor
[tex]\\ \sf\longmapsto x^2-6x+8=0[/tex]
[tex]\\ \sf\longmapsto x^2-4x-2x+8=0[/tex]
[tex]\\ \sf\longmapsto x(x-4)-2(x-4)=0[/tex]
[tex]\\ \sf\longmapsto (x-4)(x-2)=0[/tex]
[tex]\\ \sf\longmapsto x-4=0\:or\:x-2=0[/tex]
[tex]\\ \sf\longmapsto x=4\:or\:x=2[/tex]
Hence all zeros are
