The polynomials that have (x - 4) as a factor are:
n(x) = 2x^3 – 2x^2 – 20x – 16
m (x) = 2x^3 – 6x^2 – 5x – 12
f(x) = x³ – 13x – 12
Hence the correct options are b, d and e.
To determine whether (x - 4) is a factor of a polynomial, you can use synthetic division or polynomial long division. If the result is 0, then (x - 4) is a factor. Let's evaluate each polynomial:
n(x) = 2x^3 – 2x^2 – 20x – 16
Synthetic division or long division of Bn(x) by (x - 4) results in a remainder of 0, indicating that (x - 4) is a factor.
m(x) = 2x^3 – 6x^2 – 5x – 12
Again, performing synthetic division or long division on Dm(x) by (x - 4) yields a remainder of 0, confirming that (x - 4) is a factor.
f(x) = x^3 – 13x – 12
Similarly, applying synthetic division or long division to Ef(x) by (x - 4) results in a remainder of 0, indicating that (x - 4) is a factor.
For polynomials Bn(x), Dm(x), and Ef(x), (x - 4) is a factor, as the remainder is 0 when divided by (x - 4). This implies that (x - 4) evenly divides each of these polynomials, making it a factor for all three. Hence the correct options are b, d and e.