\tt\huge\red{Please \: help \: me!}

Question

asked Nov 11, 2022 6.2k views

1 Answer

Daan Seuntjens · Answer 1 · 2022-11-17T03:45:35+0000

First find Divisor

$\\ \sf\longmapsto x^2-(-3-2)+(-3)(-2)$

$\\ \sf\longmapsto x^2+5x+6$

Dividend given by

$\\ \sf\longmapsto x^4-x^3-16x^2+4x+48$

We know

$\boxed{\sf Dividend=Divisor* Quotient +Remainder}$

$\\ \sf\longmapsto Dividend=Divisor* Quotient$

$\\ \sf\longmapsto Quotient=(Dividend)/(Divisor)$

$\\ \sf\longmapsto (x^4-x^3-16x^2+4x+48)/(x^2+5x+6)$

$\\ \sf\longmapsto x^2-6x+8$

Now factor

$\\ \sf\longmapsto x^2-6x+8=0$

$\\ \sf\longmapsto x^2-4x-2x+8=0$

$\\ \sf\longmapsto x(x-4)-2(x-4)=0$

$\\ \sf\longmapsto (x-4)(x-2)=0$

$\\ \sf\longmapsto x-4=0\:or\:x-2=0$

$\\ \sf\longmapsto x=4\:or\:x=2$

Hence all zeros are