find the domain for f(x)=(2x+7)/(x^3-5x^2-4x+20)
so i have factored the denominator by grouping to get: (x^3-5x^2)-(4x+20)
Factor out x^2 and 4 : x^2(x-5)-4(x+5)
you get : (x^2-4) (x+5) (x-5)
factor x^2-4 (difference of squares) : (x+2) (x-2) (x+5) (x-5)
so because all of these are in the denominator it would stand to reason that none of these can equal zero so the domain must be: (-infinity,-5)U(-5,-2)U(-2,2)U(2,infinity), how ever, my answer key in my book says (-infinity,-2)U(-2,2)U(2,infinity) if yall could help me itd be much appreciated thank you.
so i have factored the denominator by grouping to get: (x^3-5x^2)-(4x+20)
Factor out x^2 and 4 : x^2(x-5)-4(x+5)
you get : (x^2-4) (x+5) (x-5)
factor x^2-4 (difference of squares) : (x+2) (x-2) (x+5) (x-5)
so because all of these are in the denominator it would stand to reason that none of these can equal zero so the domain must be: (-infinity,-5)U(-5,-2)U(-2,2)U(2,infinity), how ever, my answer key in my book says (-infinity,-2)U(-2,2)U(2,infinity) if yall could help me itd be much appreciated thank you.