Question

Verify that the given binomial is a factor of the polynomial using any method. p(x) = n^3 - n^2 - 6n - 24;(n - 4) a) Long Division

b) Synthetic Division
c) Factor Theorem
d) Remainder Theorem

Answer 1

To verify if the given binomial (n - 4) is a factor of the polynomial p(x) = n^3 - n^2 - 6n - 24, we can use the synthetic division method. Perform synthetic division and observe if the remainder is zero.

Step-by-step explanation:

To verify if the given binomial (n - 4) is a factor of the polynomial p(x) = n^3 - n^2 - 6n - 24, we can use the synthetic division method. Here are the steps:

1. Write the polynomial in descending order of degrees: p(x) = n^3 - n^2 - 6n - 24.
2. Set up the synthetic division table, placing the binomial divisor (n - 4) on the left and the coefficients of the polynomial on the right.
3. Perform the synthetic division by dividing each coefficient by the leading coefficient of the binomial divisor:

4 | 1 -1 -6 -24
-0
4 12 24
------
1 3 6 0

The remainder is 0, which means that (n - 4) is a factor of the polynomial p(x).