Question

Find the quatient when (x)= xcube+3xsquare+3x+5 is divided by g(x)=x+2, also find the remainder.

Answer 1

Here's your answer !!

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$g(x) = x + 2$

$= > x + 2 = 0 \\ = > x = - 2$

Now,

$g(x) = {x}^{3} + 3 {x}^{2} + 3x + 5$

$g( - 2) = {( - 2)}^{3} + 3 {( - 2)}^{2} + 3( - 2) + 5$

$g( - 2) = - 8 + 12 - 6 + 5$

$g( - 2) = 4 - 6 + 5$

$g( - 2) = 4 - 1$

$g( - 2) = 3$

Hence,

$3 \: is \: the \: remainder \: when \: {x}^{3} +3 {x}^{2}+3x+5 \\ is \: divided \: by \:(x + 2)$

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Hope it helps you !! :)

Answer 2

Answer :
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since,

let, p(x) = x³ + 3x² + 3x + 5

we have to divide it by g(x).

and, g(x) = x + 2 (given)

so,

x + 2 = 0

=> x = 0 -2

=> x = -2

then,

p(-2) = (-2)³ + 3(-2)² + 3(-2) + 5

=> p(-2) = -8 + 3×4 - 6 + 5

=> p(-2) = -8 + 12 - 1

=> p(-2) = -8 + 11

=> p(-2) = 3 ..... answer!

$\boxed{thus,\: remainder\: is \:3.}$

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