6x4-5t3-200t-163000

how do you factor this

it cant be done by common factor or decomposition method..help!!

To make sure the polynomial can be factored at all, I "cheated" and used this site:

http://firstyear.chem.usyd.edu.au/calculators/quartic.shtml

It cannot be factored into monomials with real rational constants.

The four roots of
6x^4-5t^3-200t-163000 = 0
are
13.10, -12.59
and
0.1577 +/- 12.83i

Approximate factors are:
6(x-13.10)(x+12.59)(x -0.1577 -12.83i)(x-0.1577 +12.83i)

5x^2-35+60

To factor the expression 6x^4 - 5t^3 - 200t - 163000, we can try using the rational root theorem and synthetic division to identify possible rational roots. However, it's important to note that sometimes expressions cannot be factored using rational numbers.

Step 1: List all the possible rational roots:
The possible rational roots of the expression are all the divisors of the constant term (-163000) divided by the divisors of the leading coefficient (6). In this case, the divisors of 6 are ±1, ±2, ±3, and ±6, and the divisors of -163000 are ±1, ±2, ±4, ±5, ±8, ±10, ±20, ±25, ±40, ±50, ±100, ±125, ±163, ±200, ±250, ±326, ±400, ±500, ±652, ±816, ±1000, ±1630, ±2000, ±3260, ±4080, ±5000, ±8159, ±8160, ±10000, ±16318, ±16320, ±20400, ±25000, ±32600, ±40800, ±50000, ±65200, ±81600, ±100000, ±130400, ±163000. You can use trial and error to find the roots or use a calculator or software that can find the roots for you.

Step 2: Use synthetic division to test the possible roots:
Choose one of the possible rational roots and perform synthetic division to see if it is a root:

Let's say we want to test the root 2.

2 | 6 0 -5 -200 -163000
| 12 24 38 -324 -44848
-----------------------------------
| 6 12 19 -162 -207648

The remainder is not zero, which means 2 is not a root of the equation. Repeat this step for the remaining possible rational roots until you find a root.

Step 3: Factor the expression using the root you found:
If you find a root from the previous step, let's say you find a root at t = -3, then the factor is (t + 3). To factor further, divide the original equation by the factor you found using long division or synthetic division. Then continue factoring.

In this case, if we found a root at t = -3, we divide (t + 3) by the original equation.
(6x^4 - 5t^3 - 200t - 163000) / (t + 3) = 6x^4 - 5t^2 + 15t - 65400

Now we have a new equation to factor further. Repeat Steps 1-3 until you cannot factor the expression anymore.

Keep in mind that it is possible that the expression cannot be factored using rational numbers, in which case you may need to consider other methods such as factoring by grouping or using more advanced factoring techniques.