How do you factor #x^3 - 2x^2 + 3x -6 = 0# by grouping?

Answer 1

=#(x-2)(x^2 +3)#

There are 4 terms, but there is no common factor in all of the terms. Group them into pairs to create a common factor. There must be a + sign between the pairs. This can be changed later if necessary.

#(x^3 - 2x^2) + (3x -6) = 0" look for common factors"#

=#x^2(x -2) +3(x-2) " there is a common bracket"#

=#(x-2)(x^2 +3)#

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Answer 2

Eli Assouline

To factor the polynomial x^3 - 2x^2 + 3x - 6 = 0 by grouping, you can group the first two terms together and the last two terms together.

(x^3 - 2x^2) + (3x - 6) = 0

Factor out the common factor from each group:

x^2(x - 2) + 3(x - 2) = 0

Now, notice that (x - 2) is a common factor, so factor it out:

(x^2 + 3)(x - 2) = 0

The factored form of the polynomial is (x^2 + 3)(x - 2) = 0.

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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.