Question

Hey can anyone help me with The values in the table below were taken from the graph of a 3rd-degree polynomial function.

Answer 1

The values in the table below were taken from the graph of a 3rd-degree polynomial function.


x −3 −2 −1 0 2
P(x) 0 −20 0 30 0


Which of the following represents the equation of the polynomial function?
P(x) = (x − 1)(x − 3)(x + 2)
P(x) = −5(x + 1)(x + 3)(x − 2)
P(x) = (x + 1)(x + 3)(x − 2)
P(x) = 5(x + 1)(x + 3)(x − 2)

Answer 2

They want you to know that if a polynomial is zero at x= a
then (x-a) is a factor of the polynomial

for example if we had
x^2 -3x + 2 = 0
and we factor it into
(x-1)(x-2) = 0
it should be clear that if x=1 then (x-1) becomes (1-1) = 0
and 0 * (1-2) = 0

or putting x=1 into the original
x^2 -3x + 2 = 0
1 - 3*1 + 2 = 0
1 -3 +2 = 0
-2+2 = 0
0 = 0
we get zero (as we expected)

Answer 3

In your problem you have
x −3 −2 −1 0 2
P(x) 0 −20 0 30 0

and if we look only at the places where P(x) is 0

x −3 −1 2
P(x) 0 0 0
we have 3 places: x= -3 , x= -1 and x= 2
that means the 3 factors are
(x- -3), (x- -1) and (x- 2)
they simplify (using minus a minus is plus) to
(x+3)(x+1)(x-2)

so the correct answer must have those 3 factors.

Answer 4

that means we can cross off the first choice.
3 choices remain.

to figure out which of the 3 is correct, I would use this info
x=0, P(x) = 30
(when x is 0, we should get 30)

so in each of the 3 choices, replace x with 0 and simplify
if you don't get 30, cross off that choice.