document.write( "Question 54779: Maybe I missed this part of the lecture, but I just can't figure these out. Here are two examples. Thank you very much.\r
\n" ); document.write( "\n" ); document.write( "(A) Factor 18x^7 – 12x^4 in the form of ax^b(cx^d + e), where a, b, c, d, and e are integers and a > 0. Put integers a, b, c, d and e in the 1st, 2nd, 3rd, 4th and 5th answer boxes, respectively.\r
\n" ); document.write( "\n" ); document.write( "(B) Factor 15x^8 + 10x^5 – 35x^2 in the form of ax^b(cx^d + ex^f + g), where a, b, c, d, e, f and g are integers and a, b > 0, d > f > 0. Put a, b, c, d, e, f, and g in the 1st, 2nd, 3rd, 4th, 5th, 6th and 7th answer boxes, respectively. \n" ); document.write( "

Algebra.Com's Answer #37245 by Earlsdon(6294) $\"\"$ $\"About$

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Factor:
\n" ); document.write( "A) $\"18x%5E7+-+12x%5E4\"$ Look for common multiples in each term: Looking at 18 and 12, the GCM is 6 because: 3(6) = 18 and 2(6) = 12 so you can factor 6 from the expression.
\n" ); document.write( "Now look at the variables (x's), $\"x%5E7\"$ and $\"x%5E4\"$ The GCM would be $\"x%5E4\"$ because: $\"%28x%5E4%29%28x%5E3%29+=+x%5E7\"$ and $\"%28x%5E4%29%28x%5E0%29+=+x%5E4\"$ ( $\"x%5E0+=+1\"$ ) so you can factor $\"x%5E4\"$ from the expression. Putting it all together, you get:
\n" ); document.write( " $\"18x%5E7+-+12x%5E4+=+6x%5E4%283x%5E3-2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Do you see the idea here?\r
\n" ); document.write( "\n" ); document.write( "B) $\"15x%5E8+%2B+10x%5E5+-+35x%5E2\"$ For the integers, the GCM would be 5 because: 15 = 5(3), 10 = 5(2), and 35 = 5(7)
\n" ); document.write( "For the x's the GCM would be $\"x%5E2\"$ because: $\"x%5E8+=+%28x%5E2%29%28x%5E6%29\"$ , $\"x%5E5+=+%28x%5E2%29%28x%5E3%29\"$ , and $\"x%5E2+=+%28x%5E2%29%28x%5E0%29\"$ ( $\"x%5E0+=+1\"$ ) Putting it all together, you get:
\n" ); document.write( " $\"15x%5E8+%2B+10x%5E5+-+35x%5E2+=+5x%5E2%283x%5E6+%2B+2x%5E3+-+7%29\"$ \n" ); document.write( "

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