Factor of 15(X2 +2xy)

1.	Factor of 15(X2 +2xy)
Answer» ong>Answer: Step-by-step explanation: Start by factoring 15x2+2xy−24y2 and then HOPE for the best. FACTOR this by decomposition or by magic. Note that 15×24=360 . So we seek two NUMBERS with product being 360 and difference 2 with the larger assigned a positive sign. The numbers are 20 and 18 . So continue in the following way: 15x2+2xy−24y2=15x2+20xy−18xy−24y2=5x(3x+4y)−6y(3x+4y)=(5x−6y)((3x+4y). Now for the hoping part. The −6 could mess the whole THING up. In fact, had it been some other number, the quadratic would not factor. Here’s what we do. SET y=0 and factor the result. The factored form is (5x+3)(3x−2) with the important numbers being 3 and −2 . This suggests that 15x2+2xy−24y2−x+24y−6=(5x−6y+3)(3x+4y−2) .

Answer»

ong>Answer:

Step-by-step explanation: Start by factoring 15x2+2xy−24y2 and then HOPE for the best. FACTOR this by decomposition or by magic.

Note that 15×24=360 . So we seek two NUMBERS with product being 360 and difference 2 with the larger assigned a positive sign. The numbers are 20 and 18 . So continue in the following way:

15x2+2xy−24y2=15x2+20xy−18xy−24y2=5x(3x+4y)−6y(3x+4y)=(5x−6y)((3x+4y).

Now for the hoping part. The −6 could mess the whole THING up. In fact, had it been some other number, the quadratic would not factor. Here’s what we do. SET y=0 and factor the result. The factored form is (5x+3)(3x−2) with the important numbers being 3 and −2 . This suggests that

15x2+2xy−24y2−x+24y−6=(5x−6y+3)(3x+4y−2) .

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