Question

Binomial (-2x - 8) and trinomial (-3x^2 + 4x + 5) are the factors of which of the following polynomials?

Option A: 3x^3 - 10x^2 - 49x - 40
Option B: 3x^3 - 14x^2 - 49x - 40
Option C: 3x^3 - 14x^2 - 55x - 40
Option D: 3x^3 - 10x^2 - 55x - 40

Answer 1

The given polynomial can be factored into a binomial and a trinomial. The correct option is D: 3x^3 - 10x^2 - 55x - 40.

Step-by-step explanation:

The given polynomial is 3x^3 - 10x^2 - 49x - 40. The binomial factor (-2x - 8) can be factored out by applying the distributive property. Dividing the polynomial by the binomial factor results in a trinomial factor of (3x^2 + 4x + 5). Therefore, the factors are (-2x - 8) and (3x^2 + 4x + 5).

Now, let's check which option matches the factors:

1. 3x^3 - 10x^2 - 49x - 40
2. 3x^3 - 14x^2 - 49x - 40 **(incorrect)**
3. 3x^3 - 14x^2 - 55x - 40
4. 3x^3 - 10x^2 - 55x - 40

The correct option is

D: 3x^3 - 10x^2 - 55x - 40

as it has the binomial and the trinomial factors.