Final answer:
To divide the polynomial (x³+4x²+5x+2) by (x+1), use long division to repeatedly subtract the multiples of the denominator from the numerator until the remainder has a degree less than that of the denominator or is zero.
Step-by-step explanation:
To divide the polynomials (x³+4x²+5x+2)/(x+1), you use long division or synthetic division. In this case, we will use long division.
First, you divide the first term of the numerator by the first term of the denominator, which is x³/x = x². Multiply this term by the denominator and subtract the result from the original polynomial. Next, bring down the next term and repeat this process until you have no remainder or until the degree of the remaining polynomial is less than the degree of the denominator.
By performing these steps, the division yields:
- x² (multiplied by the denominator yields x³+x²)
- Repeat the original step: 3x²/x = 3x.
- Continue these steps until the remaining polynomial's degree is less than the degree of x+1.
The final answer will be a polynomial of degree less than the denominator, or possibly a zero remainder.