factor completely (show and describe each step please)?

Question

x^3-2x^2-4x-8

Answer 1

Will you please check up and inform if there is some mistakes in sign( + /-) in one of the terms)

Answer 2

x^3 - 2x^2 - 4x - 8

Group the first two and last two terms:

(x^3 - 2x^2) + (-4x - 8)

Note the + before the parentheses. You need to do that so you factor correctly.

Now, factor out like terms from each set of parentheses:
(x^3 - 2x^2) + (-4x - 8)
x^2(x - 2) + (-4)(x + 2)

Stop right there... This isn't going to factor. Did you have a typo in the original question??
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Assume you meant
x^3 - 2x^2 - 4x + 8

Group the first two and last two terms:

(x^3 - 2x^2) + (-4x + 8)

Note the + before the parentheses. You need to do that so you factor correctly.

Now, factor out like terms from each set of parentheses:
(x^3 - 2x^2) + (-4x + 8)
x^2(x - 2) + (-4)(x - 2)

Now, you can factor the (x-2) out of each term:
(x - 2)(x^2 - 4)

You can also factor the (x^2 - 4). That's the difference of squares rule:
(a^2 - b^2) = (a - b)(a + b)

so:
x^2 - 4 = x^2 - 2^2 = (x - 2)(x + 2)

So:
(x - 2)(x^2 - 4)
= (x - 2)(x - 2)(x + 2)
= (x - 2)^2 (x + 2)

Answer 3

x^3-2x^2-4x-8 = x^2(x-2)-4(x+2)

Are you sure that it's -8 and not +8 ? If +8, then

X^2(x-2)-4(x-2) = (x^2-4)(x-2)

Answer 4

x³-2x²-4x-8
Factoring:
x²(x - 2) - 4(x - 2) =
(x² - 4)(x-2) =
(x - 2)(x + 2)(x - 2)
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Answer 5

*discover the least straightforward element... 6(x² + 4x – 21) *multiply the 1st & third variable (= -21). 2 numbers that provide you -12 whilst accelerated & 4(center) whilst further/subtracted (7 & -3) x² + 7x – 3x – 21 (x² + 7x) – (3x – 21) x(x + 7) – 3(x + 7) *do no longer forget approximately the least straightforward element. 6(x+7)(x - 3)