Question

Solve the binomial divisor equal to zero. Perform the following divisions using Sy Is the binomial divisor a factor of the polynomial, (p⁴+5p³-11p²-25p+29)-:(p+6)

Answer 1

To determine if the binomial divisor, (p+6), is a factor of the polynomial, (p⁴+5p³-11p²-25p+29), you can perform polynomial long division.

Step-by-step explanation:

To determine if the binomial divisor, (p+6), is a factor of the polynomial, (p⁴+5p³-11p²-25p+29), we can perform polynomial long division. Here's how:

1. Divide the leading term of the polynomial, p⁴, by the leading term of the divisor, p, to get p³.
2. Next, multiply the entire divisor, p+6, by p³ to get p⁴+6p³.
3. Subtract this result from the original polynomial to get the remainder: 4p³-11p²-25p+29.
4. Repeat the process of dividing the leading term of the remainder by the leading term of the divisor and subtracting the resulting term multiplied by the divisor. Keep doing this until the degree of the remainder is less than the degree of the divisor.

By following this process, you'll be able to determine whether the binomial divisor is a factor of the polynomial or not.