# How do you factor #-6cf + 8c^2d - 9df + 12cd^2#?

Given:

Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping:

The remaining quadratic term is irreducible.

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To factor the expression -6cf + 8c^2d - 9df + 12cd^2, you can factor by grouping:

Group the terms with common factors: (-6cf + 8c^2d) + (-9df + 12cd^2)

Factor out the common factors from each group: -2c(3f - 4cd) - 3d(3f - 4cd)

Factor out the common binomial factor: (-2c - 3d)(3f - 4cd)

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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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