How do you factor # x^3+8x^2+19x+12#?

Answer 1

#x^3+8x^2+19x+12 = (x+1)(x+3)(x+4)#

#f(x) = x^3+8x^2+19x+12#
Note that the coefficients of #f(-x) = -x^3+8x^2-19x+12# add up to #0#.
So #f(-1) = 0# and #(x+1)# is a factor:
#x^3+8x^2+19x+12 = (x+1)(x^2+7x+12)#
Then notice that #3+4=7# and #3xx4#=12#

Hence:

#x^2+7x+12 = (x+3)(x+4)#

Putting it all together:

#x^3+8x^2+19x+12 = (x+1)(x+3)(x+4)#
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Answer 2

To factor the expression (x^3 + 8x^2 + 19x + 12), you can use a combination of techniques such as grouping and trial and error.

First, look for any common factors among the terms, but in this case, there are none.

Next, you can try to factor by grouping.

Group the terms:

(x^3 + 8x^2) + (19x + 12)

Factor out the greatest common factor from each pair:

(x^2(x + 8)) + (1(19x + 12))

Now, look for common factors between the two groups, but there are none.

Therefore, the expression (x^3 + 8x^2 + 19x + 12) cannot be factored further using simple algebraic techniques. It may be possible to factor it using more advanced methods, but it does not appear to have any obvious linear factors.

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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.

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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