Question

Which of the following represents the factorization of the polynomial function graphed below? (Assume it has no constant factor.)

PLEASE HELP NEED ANSWER ASAP!

Answer 1

B

Explanation:

From the graph the roots are x = 1 and x = 3, hence

(x - 1) and (x - 3) are the factors of the polynomial and the polynomial is the product of the factors, that is

y = a(x - 1)(x - 3) ← a is a multiplier , here a = 1, thus

y = (x - 1)(x - 3) → B

Answer 2

Option: B is the correct answer.

B)
`y=(x-1)(x-3)`

Explanation:

From the graph that is provided to us, we see that the graph passes through .

the points (1,0) and (3,0).

This means that the zero of the function are at x=1 and at x=3

Hence, when x=1 then y=f(x)=0

and similarly

at x=3 we have f(x)=0

Now, we will check in each of the given options:

A)

`y=(x+1)(x-3)`

when x=1 then, we have:

`y=(1+1)(1-3)\\\\\\y=2* -2\\y=-4\\eq 0`

Hence, option: B is incorrect.

C)

`y=(x-1)(x+3)`

when x=3 then, we have:

`y=(3-1)(3+3)\\\\\\y=2* 6\\y=12\\eq 0`

Hence, option: C is incorrect.

D)

`y=(x+1)(x+3)`

when x=3 then, we have:

`y=(3+1)(3+3)\\\\\\y=4* 6\\y=24\\eq 0`

Hence, option: D is incorrect.

B)

`y=(x-1)(x-3)`

at x=1 and at x=3 we get y=0

Also, the graph of this function matches the given graph.

Hence, the correct answer is option: B