SOLUTION: 2x2 + bx – 15 Find all positive and negative integers b for which the polynomial can be factored.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 2x2 + bx – 15 Find all positive and negative integers b for which the polynomial can be factored.      Log On


   

Question 227692: 2x2 + bx – 15 Find all positive and negative integers b for which the polynomial can be factored.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
An expression like 2x%5E2%2Bbx-15, if it factors at all, will factor into the form: %28a%5B1%5D%2Ax+%2B+c%5B1%5D%29%28a%5B2%5D%2Ax+%2B+c%5B2%5D%29 where a%5B1%5D and a%5B2%5D are factors of the 2 and c%5B1%5D and c%5B2%5D are factors of the -15. And the b+=+a%5B1%5D+%2A+c%5B2%5D+%2B+a%5B2%5D%2Ac%5B1%5D

So to find all the possible b's we need to find the factors of 2 and -15:
Factors of 2:
1 and 2
Factors of -15:
-1 and 15
1 and -15
3 and -5
-3 and 5
Now we just use all the possible combinations of factors of 2 and factors of -15 in b+=+a%5B1%5D+%2A+c%5B2%5D+%2B+a%5B2%5D%2Ac%5B1%5D:
  • b+=+1%2A%28-1%29+%2B+2%2A15+=+-1+%2B+30+=+29
  • b+=+1%2A%2815%29+%2B+2%2A%28-1%29+=+15+%2B+-2+=+13
  • b+=+1%2A1+%2B+2%2A%28-15%29+=+1+%2B+%28-30%29+=+-29
  • b+=+1%2A%28-15%29+%2B+2%2A1+=+-15+%2B+2+=+-13
  • b+=+1%2A%283%29+%2B+2%2A%28-5%29+=+3+%2B+%28-10%29+=+-7
  • b+=+1%2A%28-5%29+%2B+2%2A3+=+-5+%2B+6+=+1
  • b+=+1%2A%28-3%29+%2B+2%2A5+=+-3+%2B+10+=+7
  • b+=+1%2A5+%2B+2%2A%28-3%29+=+5+%2B+%28-6%29+=+-1