SOLUTION: {{{12b^4+36b^3-20b^2}}} i really dont get how to factor the polynomial can you help[ me plz.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{12b^4+36b^3-20b^2}}} i really dont get how to factor the polynomial can you help[ me plz.      Log On


   

Question 568309: 12b%5E4%2B36b%5E3-20b%5E2 i really dont get how to factor the polynomial can you help[ me plz.
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
12b%5E4%2B36b%5E3-20b%5E2
the first step is to see if there is something we can factor out from each term.
If I rewrite everything like this, its more clear
12%2Ab%2Ab%2Ab%2Ab%2B36%2Ab%2Ab%2Ab-20%2Ab%2Ab
or if I do a prime factorization of each number like this:
3%2A2%2A2%2Ab%2Ab%2Ab%2Ab%2B3%2A3%2A2%2A2%2Ab%2Ab%2Ab-2%2A2%2A5%2Ab%2Ab
So each term has 2*2*b*b which is 4b^2
so I need to factor out 4b^2 from each term
4b^2*(3b^2+9b-5)
and we can factor further if need be but you can probably stop here.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B9x%2B-5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%289%29%5E2-4%2A3%2A-5=141.

Discriminant d=141 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+141+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+141+%29%29%2F2%5C3+=+0.479057014506319
x%5B2%5D+=+%28-%289%29-sqrt%28+141+%29%29%2F2%5C3+=+-3.47905701450632

Quadratic expression 3x%5E2%2B9x%2B-5 can be factored:
3x%5E2%2B9x%2B-5+=+3%28x-0.479057014506319%29%2A%28x--3.47905701450632%29
Again, the answer is: 0.479057014506319, -3.47905701450632. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B9%2Ax%2B-5+%29