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How do you factor #a^3 - 2a^2 - 4a = -8#?

Answer 1

Julia Adams

You must mean to ask how to solve the equation.

Put everything to one side of the equation:

#a^3 - 2a^2 - 4a + 8 = 0#

Factor out a common factor from two groups: the first 2 terms and last 2 terms.

#a^2(a - 2) - 4(a - 2) = 0#

#(a^2 - 4)(a - 2) = 0#

#(a + 2)(a - 2)(a - 2) = 0#

#a = -2 and 2#

The polynomial is completely factored and the solution set is #a = +-2#.

Hopefully this helps.

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Answer 2

Eli Assouline

To factor the expression (a^3 - 2a^2 - 4a = -8), follow these steps:

Rewrite the equation as (a^3 - 2a^2 - 4a + 8 = 0).
Factor out the greatest common factor, which is 1: (a(a^2 - 2a - 4) + 8 = 0).
Factor the quadratic expression (a^2 - 2a - 4) using the quadratic formula or factoring techniques. The factors are ((a - 2)(a + 2)).
Rewrite the expression with the factored quadratic: (a(a - 2)(a + 2) + 8 = 0).
The factors of the equation are (a(a - 2)(a + 2) + 8 = 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.