Question

State if the given binomial is a factor of the given polynomial. (m – 3m2 – m+26) = (m+2)

Yes
No

Answer 1

To check if (m+2) is a factor of (m – 3m2 – m+26), we need to divide the polynomial by (m+2) using synthetic division. If the final result is zero, it means that (m+2) is a factor of the given polynomial. If the result is non-zero, then (m+2) is not a factor.

Step-by-step explanation:

The given binomial is (m+2) and the given polynomial is (m – 3m2 – m+26).

To check if (m+2) is a factor of (m – 3m2 – m+26), we need to divide the polynomial by (m+2) using synthetic division.

Write the coefficients of the polynomial in descending order: -3, -1, 0, 26.

Using synthetic division, divide the polynomial:

Bring down the first coefficient (-3) and multiply it by the divisor, 2.

Add the result to the next coefficient, -1. Repeat this process until the last coefficient.

The final result should be zero.

If the final result is zero, it means that (m+2) is a factor of the given polynomial. If the result is non-zero, then (m+2) is not a factor.

In this case, the final result is not zero, so (m+2) is not a factor of (m – 3m2 – m+26).