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

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) (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)

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.

The RANGE for the rational expression is ALL REAL NUMBERS.
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