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When factoring you use any and all factorign methds to factor until there is nothing else that will factor:
- .The GCF is 1 which we don't usually bother factoring out.
- The factoring patterns all have either 2 or 3 terms. Your expression has 4. So we cannot use the patterns.
- Trinomial factorin, as the \"tri\" suggest, works on expressions of 3 terms. SO we cannot it on your 4-term expression.
- Factoring by grouping requires and even number of terms so there is some hope.
\n" ); document.write( "When factoring by grouping you break up the expression into sub-expressions, factor out the GCF from each sub-expression and hope that the non-GCF factors match. You may have to re-order and re-group the terms to make this work. Let's first try your expression, as is:
\n" ); document.write( "vy+15v+5y+3v^2
\n" ); document.write( "Grouping:
\n" ); document.write( "(vy+15v) + (5y+3v^2)
\n" ); document.write( "The GCf in the first group is \"v\" and the GCF of the second group is 1. (Note: This part of factoring by grouping is one of the few times when you actually factor out a GCF of 1!) Factoring these GCF's out we get:
\n" ); document.write( "v(y+15) + 1(5y+3y^2)
\n" ); document.write( "The \"non-GCF\" factors, (y+15) and (5y+3y^2), do not match. (We want them to match.) So we must try again.
\n" ); document.write( "Let's try re-ordering and re-grouping:
\n" ); document.write( "(vy+3v^2) + (15v + 5y)
\n" ); document.write( "The GCF's are \"v\" and 5. Factoring them out we get:
\n" ); document.write( "v(y+3v) + 5(3v+5)
\n" ); document.write( "The \"non-GCF\" factors are (y+3v) and (3v+y). Since order does not matter when adding, they match! So we can continue with the factoring. We factor out the \"non-GCF\" factor:
\n" ); document.write( "(y+3v)(v+5)
\n" ); document.write( "Since neither factor will factor any further, no matter which method we try, we are finished factoring. \n" ); document.write( "