Question

`\tt\huge\red{Please \: help \: me!}`
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Answer 1

First find Divisor

• Two zeros are -3,-2

`\\ \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}`

• Remainder is 0

`\\ \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

• 2,-2,-3,4