document.write( "Question 583689: Can you please help me solve this? $\"%2816x%5E5+-+32x%5E4+-+81x+%2B+162%29+%2F+%28x+-+2%29\"$ I am supposed to solve and state whether the binomial is a factor of the polynomial.\r
\n" ); document.write( "\n" ); document.write( "I used synthetic division to drop the coefficients and got: \r
\n" ); document.write( "\n" ); document.write( "2] 16 -32 0 0 -81 162
\n" ); document.write( " 0 32 0 0 0 -162
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\n" ); document.write( " 16 0 0 0 0 -81 0
\n" ); document.write( "(The zeroes in the top row are because there are no x-cubed and x-squared variables, therefore they're respresented by a zero, right?)\r
\n" ); document.write( "\n" ); document.write( "Multiple choice allowed me the answers of:
\n" ); document.write( "A - 1348; no
\n" ); document.write( "B - 0; yes
\n" ); document.write( "C - 700; yes
\n" ); document.write( "D - 0; no\r
\n" ); document.write( "\n" ); document.write( " I am pretty sure the answer is C because my remainder is zero, and x-2 is a factor of the original equation. If this is not right, can you please show me what I've done wrong?
\n" ); document.write( "(Also, I apologize if the synthetic division does not line up properly when submitted and if it makes it harder for you to read.) \n" ); document.write( "

Algebra.Com's Answer #372540 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The numerator can be factored by grouping; no synthetic division required:\r\n" );
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document.write( "Factor 16x⁴ out of the first two terms and -81 out of the last two terms:\r\n" );
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document.write( "Now factor (x-2) out of the two terms in the numerator:\r\n" );
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document.write( "That's enough to show that the binomial x-2 is a factor of numerator and\r\n" );
document.write( "denominator.  However let's finish factoring. We can factor  as\r\n" );
document.write( "the difference of squares:\r\n" );
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document.write( "We can further factor  as the difference of squares:\r\n" );
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document.write( "And as long as x isn't 2, we can cancel the (x-2)'s and get\r\n" );
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document.write( "Edwin

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