What is the solution set for #-x^3-2x^2=-x-2#?

Answer 1

The solution set is #x={-2,-1,1}#

#-x^3-2x^2=-x-2#
Multiply the equation times #-1#.
#x^3+2x^2=x+2#
Move all terms to the left side by subtracting #x+2# from both sides.
#x^3+2x^2-x-2=0#

Group the terms into two binomials.

#(x^3+2x^2)-(x+2)#
Factor out #x^2# from the first group.
#x^2(x+2)-(x+2)#
Factor out #(x+2)#.
#(x^2-1)(x+2)#
#(x^2-1)# can be factored as the difference of squares.
#(x^2-1)=(x+1)(x-1)#
The complete factorization of #-x^3-2x^2=-x-2# is #(x+2)(x+1)(x-1)=0#.
Since the factors are equal to zero, we must set each one equal to zero, and solve for #x#.
#x+2=0# #x=-2#
#x+1=0# #x=-1#
#x-1=0# #x=1#
The solution set is #x={-2,-1,1}#
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Answer 2

The solution set for the equation -x^3 - 2x^2 = -x - 2 is {-1, 2}.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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