document.write( "Question 706025: determine p so that 4q+3 is a factor of 20q^3+23q^2-10q+p \n" ); document.write( "

Algebra.Com's Answer #434933 by jsmallt9(3758) $\"\"$ $\"About$

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If we factor a 4 out of 4q+3 we get
\n" ); document.write( " $\"4%28q%2B3%2F4%29\"$
\n" ); document.write( "So if (4q+3) is a factor of our polynomial then so will $\"%28q%2B4%2F3%29\"$ . This fact is useful because we can more obviously use synthetic division with the $\"%28q%2B3%2F4%29\"$ :
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document.write( "-3/4 |   20   23   -10   p\r\n" );
document.write( "------       -15    -6  12 \r\n" );
document.write( "        --------------------\r\n" );
document.write( "         20    8   -16  12+p\r\n" );
document.write( "

\n" ); document.write( "In order for $\"%28q%2B3%2F4%29\"$ (and therefore (4q+3)) to be a factor, the remainder, 12+p, must be zero. So \"p\" must be -12. \n" ); document.write( "

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