document.write( "Question 1169662: Determine whether the second polynomial is a factor of the first.
\n" ); document.write( "4x^2+6x+32; x-4 \n" ); document.write( "
Algebra.Com's Answer #794449 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Let p(x) = 4x^2+6x+32\r
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\n" ); document.write( "\n" ); document.write( "If x-4 is a factor of p(x), then p(4) = 0
\n" ); document.write( "This is because x-4 = 0 leads to x = 4 as a root.\r
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\n" ); document.write( "\n" ); document.write( "So let's see if plugging x = 4 leads to 0 as a result
\n" ); document.write( "p(x) = 4x^2+6x+32
\n" ); document.write( "p(4) = 4(4)^2+6(4)+32
\n" ); document.write( "p(4) = 120
\n" ); document.write( "We get a nonzero value, so we conclude x-4 is not a factor of 4x^2+6x+32.\r
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\n" ); document.write( "\n" ); document.write( "note how each term of 4x^2+6x+32 is positive
\n" ); document.write( "4x^2 is positive
\n" ); document.write( "6x is positive
\n" ); document.write( "32 is positive
\n" ); document.write( "Plugging a positive x value into the equation leads to some positive result. We need some negatives in there to counterbalance the positives, to be able to get to 0. This is a fairly quick way to see that p(4) cannot possibly be 0.\r
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\n" ); document.write( "\n" ); document.write( "Answer: x-4 is not a factor of 4x^2+6x+32
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