document.write( "Question 719665: Show that (x-2) and (x-3) are factors of F(x)=2x^4+7x^3-4x^2-27x-18. Then find the remaining factors of f(x). \n" ); document.write( "
Algebra.Com's Answer #441449 by swincher4391(1107)\"\" \"About 
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By the factor theorem, if x-2 is a factor of f(x): 2x^4+7x^3-4x^2-27x-18, then f(2) = 0. That is to say, if we were to plug in 2, we would result in 0. \r
\n" ); document.write( "\n" ); document.write( "2(2^4) + 7(2^3) - 4(2^2)-27(2) - 18\r
\n" ); document.write( "\n" ); document.write( "32 + 56 - 16 - 54 - 18 = 0 (check).\r
\n" ); document.write( "\n" ); document.write( "I do believe that there is a typo in your question. It should read (x+3).\r
\n" ); document.write( "\n" ); document.write( "Plugging in -3 yields 0.\r
\n" ); document.write( "\n" ); document.write( "If you have not learned the factor theorem, disregard the previous work.\r
\n" ); document.write( "\n" ); document.write( "Alternative method (long division):\r
\n" ); document.write( "\n" ); document.write( "(x-2) | 2x^4 +7x^3 - 4x^2 -27x - 18\r
\n" ); document.write( "\n" ); document.write( "Going through this we get 2x^3+11x^2+18x+9, with no remainder. Since there is no remainder, x-2 factors into it evenly. You would repeat the process for x+3 into the remaining 2x^3 + 11x^2 + 18x + 9 leaving you 2x^2 + 5x + 3. This factors into (2x+3)(x+1) [remaining factors]\r
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