document.write( "Question 568309: \"12b%5E4%2B36b%5E3-20b%5E2\" i really dont get how to factor the polynomial can you help[ me plz. \n" ); document.write( "
Algebra.Com's Answer #366901 by TutorDelphia(193)\"\" \"About 
You can put this solution on YOUR website!
\"12b%5E4%2B36b%5E3-20b%5E2\"
\n" ); document.write( "the first step is to see if there is something we can factor out from each term. \r
\n" ); document.write( "\n" ); document.write( "If I rewrite everything like this, its more clear
\n" ); document.write( "\"12%2Ab%2Ab%2Ab%2Ab%2B36%2Ab%2Ab%2Ab-20%2Ab%2Ab\"
\n" ); document.write( "or if I do a prime factorization of each number like this:
\n" ); document.write( "\"3%2A2%2A2%2Ab%2Ab%2Ab%2Ab%2B3%2A3%2A2%2A2%2Ab%2Ab%2Ab-2%2A2%2A5%2Ab%2Ab\"\r
\n" ); document.write( "\n" ); document.write( "So each term has 2*2*b*b which is 4b^2\r
\n" ); document.write( "\n" ); document.write( "so I need to factor out 4b^2 from each term
\n" ); document.write( "4b^2*(3b^2+9b-5)
\n" ); document.write( "and we can factor further if need be but you can probably stop here.\r
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"3x%5E2%2B9x%2B-5+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%289%29%5E2-4%2A3%2A-5=141\".
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\n" ); document.write( " Discriminant d=141 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-9%2B-sqrt%28+141+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%289%29%2Bsqrt%28+141+%29%29%2F2%5C3+=+0.479057014506319\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%289%29-sqrt%28+141+%29%29%2F2%5C3+=+-3.47905701450632\"
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\n" ); document.write( " Quadratic expression \"3x%5E2%2B9x%2B-5\" can be factored:
\n" ); document.write( " \"3x%5E2%2B9x%2B-5+=+3%28x-0.479057014506319%29%2A%28x--3.47905701450632%29\"
\n" ); document.write( " Again, the answer is: 0.479057014506319, -3.47905701450632.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B9%2Ax%2B-5+%29\"
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