Question #e9a58

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Question #e9a58

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Answer 1 · 2017-04-12T09:21:57

$x^{3} + 2 x^{2} + 3 x + 6$ $color(blue)(x^3+2x^2+3x+6$

Explanation:

$(x + 1) (x^{2} + 3)$ $(x+1)(x^2+3)$

$a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaa)$ $x^{2} + 3$ $x^2+3$
$a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaa)$ $x + 1$ $x+1$
$a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaa)$ $- - - - -$ $-----$
$a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaa)$ $x^{3}$ $x^3$ $a a a a$ $color(white)(aaaa)$ $+ 3 x$ $+3x$
$a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaa)$ $2 x^{2}$ $2x^2$ $a a a a$ $color(white)(aaaa)$ $+ 6$ $+6$
$a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaa)$ $- - - - - -$ $------$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ $x^{3} + 2 x^{2} + 3 x + 6$ $color(blue)(x^3+2x^2+3x+6$

Answer 2 · 2017-04-12T10:00:10

$3 x^{2} + 4 x + 3$ $3x^2+4x+3$

Explanation:

$Expand the brackets$ $"Expand the brackets"$

$(x + 2) (x^{2} + 3) = x^{3} + 2 x^{2} + 3 x + 6$ $(x+2)(x^2+3)=x^3+2x^2+3x+6$

differentiate each term using the $power rule$ $color(blue)"power rule"$

$∙ \frac{d}{d x} (a x^{n}) = n a x^{n - 1}$ $• d/dx(ax^n)=nax^(n-1)$

$\Rightarrow \frac{d}{d x} (x^{3} + 2 x^{2} + 3 x + 6)$ $rArrd/dx(x^3+2x^2+3x+6)$

$= 3 x^{2} + 4 x + 3$ $=3x^2+4x+3$

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Question #e9a58

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