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S i m p l i f y : x + 4 2 x 3 − 32 x 2 − 32 x + 512 \\ Simplify:\\ \\ \Large \frac { x + 4 }{ { 2x }^{ 3 } -{ 32x }^{ 2 }-32x+512 }

1 2 ( x − 4 ) ( x + 16 ) \frac { 1 }{ 2(x\quad -\quad 4)(x\quad +\quad 16) } 1 2 ( x − 4 ) ( x − 16 ) \frac { 1 }{ 2(x\quad -\quad 4)(x\quad -\quad 16) } 1 2 ( x + 4 ) ( x − 16 ) \frac { 1 }{ 2(x\quad +\quad 4)(x\quad -\quad 16) } 1 2 ( x + 4 ) ( x + 16 ) \frac { 1 }{ 2(x\quad +\quad 4)(x\quad +\quad 16) }

Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

Ashish Menon
Apr 19, 2016

( x + 4 ) ( 2 x 3 − 32 x 2 − 32 x + 512 ) = ( x + 4 ) 2 ( x 3 − 16 x 2 − 16 x + 256 ) = ( x + 4 ) 2 ( x 2 ( x − 16 ) − 16 ( x − 16 ) = ( x + 4 ) 2 ( x 2 − 16 ) ( x − 16 ) = ( x + 4 ) 2 ( x + 4 ) ( x − 4 ) ( x − 16 ) = ( x + 4 ) 2 ( x + 4 ) ( x − 4 ) ( x − 16 ) = 1 2 ( x − 4 ) ( x − 16 ) \begin{aligned} \dfrac{(x+4)}{(2x^3 - 32x^2 - 32x + 512)} & = \dfrac{(x+4)}{2(x^3 - 16x^2 - 16x + 256)}\\ \\ & = \dfrac{(x+4)}{2(x^2(x - 16) - 16(x - 16)}\\ \\ & = \dfrac{(x+4)}{2(x^2 - 16)(x - 16)}\\ \\ & = \dfrac{(x+4)}{2(x + 4)(x - 4)(x - 16)}\\ \\ & = {\dfrac{\cancel{(x+4)}}{2\cancel{(x + 4)}(x - 4)(x - 16)}}\\ \\ & = \boxed{\dfrac{1}{2(x - 4)(x - 16)}} \end{aligned}

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So, the answer to the problem is wrong?

Angela Fajardo - 5 years, 1 month ago

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LOL, it was just a typo in the last line which I fixed 10 seconds ago, its not that the question is wrong XD

Ashish Menon - 5 years, 1 month ago

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I was nervous for a moment there

Angela Fajardo - 5 years, 1 month ago

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@Angela Fajardo – Hahaha, nvm.

Ashish Menon - 5 years, 1 month ago

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