# How do you find all zeros with multiplicities of #f(x)=x^4+2x^3-12x^2-40x-32#?

Given:

That means that the only possible rational zeros are:

graph{x^4+2x^3-12x^2-40x-32 [-10, 10, -160, 80]}

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To find all zeros with multiplicities of the polynomial ( f(x) = x^4 + 2x^3 - 12x^2 - 40x - 32 ), you can use methods like factoring, synthetic division, or the rational root theorem. Alternatively, you can use numerical methods like Newton's method or graphing to approximate the roots.

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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.

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