Question

question 5 of 5
select all the correct answers.
which of these are factors of this polynomial?
-3x³ + 15x² + 3x - 15
(x + 5)
(3x - 1)
-3
(x + 1)
(x - 1)
3x
(x - 5)

Explanation:

Step1: Factor by grouping

Group the polynomial: $(-3x^3 + 15x^2) + (3x - 15)$
Factor out common terms from each group: $-3x^2(x - 5) + 3(x - 5)$

Step2: Factor out the common binomial

Factor out $(x - 5)$: $(x - 5)(-3x^2 + 3)$

Step3: Factor the quadratic

Factor out -3 from the quadratic: $(x - 5)(-3)(x^2 - 1)$

Step4: Factor the difference of squares

Factor $x^2 - 1$ as $(x - 1)(x + 1)$: $(x - 5)(-3)(x - 1)(x + 1)$

So the factors are $-3$, $(x - 5)$, $(x - 1)$, $(x + 1)$

Answer:

-3, (x - 5), (x - 1), (x + 1) (corresponding to the options: -3, (x - 5), (x - 1), (x + 1))