SOLUTION: 1. 2x^2 +8x -24/ x^2 +x -12 Cant find range. I thought it was (negative inf, 2) and (2,inf) but it was wrong 2. t^4 -19t^2 +48 Factor the polynomial completely. I got (t+4

Algebra ->  Equations -> SOLUTION: 1. 2x^2 +8x -24/ x^2 +x -12 Cant find range. I thought it was (negative inf, 2) and (2,inf) but it was wrong 2. t^4 -19t^2 +48 Factor the polynomial completely. I got (t+4      Log On


   

Question 1039733: 1.
2x^2 +8x -24/ x^2 +x -12 Cant find range. I thought it was (negative inf, 2) and (2,inf) but it was wrong
2.
t^4 -19t^2 +48 Factor the polynomial completely. I got (t+4)(t-4)(t-sqrt 48)(t+sqrt48) this is wrong.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2 +8x -24/ x^2 +x -12
?

(2x^2 +8x -24)/(x^2 +x -12)

%282x%5E2%2B8x-24%29%2F%28x%5E2%2Bx-12%29

%282%28x%5E2%2B4x-12%29%29%2F%28%28x-3%29%28x%2B4%29%29

2%28%28x-2%29%28x%2B6%29%29%2F%28%28x-3%29%28x%2B4%29%29

You want to see what happens near the critical values of x to find the set of possible values for the expression (the range). The expression is undefined for x=3 and for x=-4. Signs just change at the zeros which are x=2 and x=-6. No factor shared in both numerator and denominator, so no missing point. Obviously NOT continuous at x=3 or x=-4.

INTERVALS to check for signs:
(-infin,-6]
([-6,-4]
[-4,2]
[2,3]
[3,infinity)

You can decide how to check how the values tend through whatever arithmetic you may be learning for handling rational functions, but I will just show a graph here for help in checking.

graph%28300%2C300%2C-8%2C6%2C-7%2C7%2C%282x%5E2%2B8x-24%29%2F%28x%5E2%2Bx-12%29%29



The RANGE for the rational expression is ALL REAL NUMBERS.