To find the quotient of the polynomial x³ + 2 – 5x + 3x – 1, we first need to rearrange and simplify the polynomial by combining like terms. So, let’s simplify it step by step:
- Combine the x terms: -5x + 3x results in -2x.
- Now the polynomial can be expressed as: x³ – 2x + 1.
Next, we can perform polynomial long division if we plan to divide this polynomial by another polynomial. However, your question does not specify a divisor. If the intent was to find the quotient from a specific divisor, please specify it.
For example, if we are dividing x³ – 2x + 1 by x – 1, we can use long division:
- Divide the leading term: x³ divided by x gives x².
- Multiply and subtract:
(x³ – 2x + 1) – (x²)(x – 1) = x³ – x²
This becomes: -2x + 1 + x², resulting in x² – 2x + 1.
Again, we would continue dividing but this gives you an initial understanding of finding the quotient. Make sure you clarify the polynomial to divide by for complete results.
In conclusion, if we did not have a divisor, the original polynomial can remain as it is: x³ – 2x + 1.