SOLUTION: choose the best answer? thanks! X^2+12x-3 A.) (X+3)(X-1) B.) (X-3)(X+1) C.) (X+3)(x+9) D.) prime

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: choose the best answer? thanks! X^2+12x-3 A.) (X+3)(X-1) B.) (X-3)(X+1) C.) (X+3)(x+9) D.) prime      Log On


   

Question 74320: choose the best answer? thanks!

X^2+12x-3
A.) (X+3)(X-1) B.) (X-3)(X+1)
C.) (X+3)(x+9) D.) prime
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you plug your quadratic into the quadratic formula, you can find the factors
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B-3+=+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=%2812%29%5E2-4%2A1%2A-3=156.

Discriminant d=156 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+156+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+156+%29%29%2F2%5C1+=+0.244997998398398
x%5B2%5D+=+%28-%2812%29-sqrt%28+156+%29%29%2F2%5C1+=+-12.2449979983984

Quadratic expression 1x%5E2%2B12x%2B-3 can be factored:
1x%5E2%2B12x%2B-3+=+1%28x-0.244997998398398%29%2A%28x--12.2449979983984%29
Again, the answer is: 0.244997998398398, -12.2449979983984. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B-3+%29

Since the zeros are irrational, there are no rational factors. So the polynomial is prime (answer d).