Final answer:
The expression x⁴-16x²-4x³+64x+3x²-48 can be rearranged but does not factor easily. Multiplying both sides by a factor or using the quadratic formula may be helpful strategies if the expression can be brought to a quadratic form.
Step-by-step explanation:
To factor the expression x⁴-16x²-4x³+64x+3x²-48, we need to rearrange and combine like terms first, resulting in x⁴-4x³+(16x²+3x²)-16x²+64x-48. This simplifies to x⁴-4x³+19x²+64x-48. There seems to be no obvious way to factor this expression by grouping or using formulas. However, you can always multiply both sides by the same factor or complete the square to make this into a form that is easier to understand or to solve for x. If the expression were to be similar to a quadratic, we would have it in the form of ax² + bx + c = 0 and could use the quadratic formula to find the values of x.