document.write( "Question 108815: We just started factoring polynomials,and I don't understand when you first look at a problem,if it has a greater common factor or not.I did read my book but I'm still confused.could you explain this to me,and possibly give me some examples.I appreciate all the help you all have given me.
\n" ); document.write( "Thanks in advance sincerely,JH \n" ); document.write( "

Algebra.Com's Answer #79312 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
The first thing that you do when factoring is take out all of the $\"Greatest-+Common-+Factor\"$ \r
\n" ); document.write( "\n" ); document.write( "Example:\r
\n" ); document.write( "\n" ); document.write( " $\"6x%B3%2B27x%B2-105x\"$ ЕЕЕ..when factor the numbers $\"6\"$ , $\"27\"$ , and
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\n" ); document.write( " $\"105\"$ , you will see that each one is divisible by $\"3\"$ . \r
\n" ); document.write( "\n" ); document.write( "Also, when you look at $\"x%5E3\"$ , $\"x%5E2\"$ , and $\"x\"$ , you will see that \r
\n" ); document.write( "\n" ); document.write( "all of them you can divide by $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( "So, the $\"greatest-+common-+factor\"$ here is $\"3x\"$ .\r
\n" ); document.write( "\n" ); document.write( "Then you can write your equation like this:\r
\n" ); document.write( "\n" ); document.write( " $\"3x%282x%5E2+%2B+9x+-+35%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Then you factor $\"%282x%5E2+%2B+9x+-+35%29\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2+%2B+9x+-+35%29\"$ Е.write $\"9x\"$ as $\"14x+-+5x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2+%2B+14x+-+5x+-+35%29\"$ ЕЕ..group first and third term, second and fourth term\r
\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2+-+5x%29\"$ + ( $\"14x\"$ Ц $\"35\"$ )ЕЕ..here, in first term common factor is
\n" ); document.write( " $\"x\"$ , and in second term common factor is $\"7\"$ \r
\n" ); document.write( "\n" ); document.write( "so, we can write it: $\"x%282x-5%29\"$ , and $\"7%282x-5%29\"$ where we see that common \r
\n" ); document.write( "\n" ); document.write( "factor is $\"2x+%96+5\"$ \r
\n" ); document.write( "\n" ); document.write( "now we can write $\"%282x-5%29%28x+%2B+7%29\"$ \r
\n" ); document.write( "\n" ); document.write( "if we go back to our equation, we can write it like this:\r
\n" ); document.write( "\n" ); document.write( " $\"3x%282x-5%29%28x%2B7%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Remember:\r
\n" ); document.write( "\n" ); document.write( "Factoring a polynomial is the $\"opposite+\"$ $\"process+\"$ of multiplying polynomials.\r
\n" ); document.write( "\n" ); document.write( "The $\"simplest\"$ type of factoring is $\"when\"$ $\"+there\"$ $\"+is\"$ a factor $\"common\"$ $\"+to\"$ $\"+every\"$ $\"+term\"$ .\r
\n" ); document.write( "\n" ); document.write( "Recall that the $\"distributive\"$ $\"+law\"$ says that $\"a%28b+%2B+c%29+=+ab+%2B+ac\"$ \r
\n" ); document.write( "\n" ); document.write( "If you see something of the form $\"a2+-+b2\"$ , you should remember the formula:
\n" ); document.write( " $\"%28a-b%29%28a%2Bb%29\"$ = $\"a%5E2\"$ Ц $\"b%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "This only holds for a $\"difference\"$ of two squares, NOT for a $\"sum\"$ of two squares such as $\"+a2+%2B+b2\"$ into factors with real numbers.\r
\n" ); document.write( "\n" ); document.write( "Remember:\r
\n" ); document.write( "\n" ); document.write( " УPerfect Square TrinomialФ
\n" ); document.write( "Recall from special products of binomials that $\"%28a+%2B+b%29%5E2+=+a%5E2+%2B+2ab+%2B+b%5E2\"$ and $\"%28a+-+b%29%5E2+=+a%5E2+-+2ab+%2B+b%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "It will help you to solve any problem. Good luck!!!!!!!!!\r
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