How do you factor #(1+x-x^2)^2#?
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To factor ( (1+x-x^2)^2 ), you can first factor the expression inside the parentheses and then square the result:
- Factor ( 1 + x - x^2 ): Rewrite it as ( -(x^2 - x - 1) ).
- Find two numbers that multiply to -1 and add up to -1. These numbers are 1 and -1.
- Rewrite the middle term (-x) using these two numbers: ( -x = x - 1x ).
- Rewrite the expression: ( -(x^2 - x - 1) = -(x^2 + x - x - 1) = -(x(x + 1) - 1(x + 1)) ).
- Factor by grouping: ( -(x(x + 1) - 1(x + 1)) = -(x + 1)(x - 1) ).
- Square the result: ( (-(x + 1)(x - 1))^2 = (x + 1)^2(x - 1)^2 ).
So, ( (1+x-x^2)^2 ) factors as ( (x + 1)^2(x - 1)^2 ).
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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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