SOLUTION: How do you factor 3x^2+490x+6000 ? Thanks. :)

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Question 435569: How do you factor 3x^2+490x+6000 ? Thanks. :)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

3x² + 490x + 6000

Use the "ac" method:

Multiply 3 by 6000

Get 18000

We write all the factor pairs of 18000
as well as the sum of the factor pairs,
and see if any give you a sum of 490

 
18000 × 1;  18000 +  1 = 18001
 9000 × 2;   9000 +  2 = 9002
 6000 × 3;   6000 +  3 = 6003
 4500 × 4;   4500 +  4 = 4504
 3600 × 5;   3600 +  5 = 3605
 3000 × 6;   3000 +  6 = 3006
 2250 × 8;   2250 +  8 = 2258
 2000 × 9;   2000 +  9 = 2009
 1800 × 10;  1800 + 10 = 1810
 1500 × 12;  1500 + 12 = 1512
 1200 × 15;  1200 + 15 = 1215
 1125 × 16;  1125 + 16 = 1141
 1000 × 18;  1000 + 18 = 1018
  900 × 20;   900 + 20 = 920
  750 × 24;   750 + 24 = 774
  720 × 25;   720 + 25 = 745
  600 × 30;   600 + 30 = 630
  500 × 36;   500 + 36 = 536
  450 × 40;   450 + 40 = 490
  400 × 45;   400 + 45 = 445
  375 × 48;   375 + 48 = 423
  360 × 50;   360 + 50 = 410
  300 × 60;   300 + 60 = 360
  250 × 72;   250 + 72 = 322
  240 × 75;   240 + 75 = 315
  225 × 80;   225 + 80 = 305
  200 × 90;   200 + 90 = 290
  180 × 100;  180 + 100 = 280
  150 × 120;  150 + 120 = 270
  144 × 125;  144 + 125 = 269

and we find that there is indeed one pair of factors, 450 and 40
with sum 490.

So we write 

3x² + 490x + 6000

as

3x² + 450x + 40x + 6000

Then we factor 3x out of the first two terms and 40 out
of the last two terms:

3x(x + 150) + 40(x + 150)

Next we factor out common factor of (x + 150)

(x + 150)(3x + 40)

What a horrible problem!

Edwin