Question

Write the equation of the graph shown below in factored form.

1. f(x) = (x − 3)(x + 1)(x + 4)
2. f(x) = (x + 3)(x − 1)(x − 4)
3. f(x) = (x + 3)(x + 1)(x + 4)
4. f(x) = (x − 3)(x − 1)(x − 4)

Answer 1

2. f(x) = (x + 3)(x − 1)(x − 4)

Explanation:

As we know that, the standard factored form of an cubic polynomial is:

f(x)= a(x -
`r_(1)`)(x -
`r_(2)`)(x -
`r_(3)`) where:
`r_(1)` ,
`r_(2)`,
`r_(3)` are the roots or x-intercept of the function when it is equal to 0.

In this situation, we can see that:

• 
  `r_(1)` = 4
• 
  `r_(2)` = 1
• 
  `r_(3)` = -3
• a = 1

So the the equation of the graph shown is:

f(x) = a(x -
`4`)(x -1)(x +3)

We choose 2, hope it will find you well.

Answer 2

2. f(x) = (x + 3)(x − 1)(x − 4)

Explanation:

The roots of this polynomial graph are the x-intercepts.

These are x=-3, x=1, x=4

These implies that the factors of the function are:

(x+3), (x-1), and (x-4)

The factored form is given as:

`f(x) = (x + 3)(x - 1)(x - 4)`

Therefore the second option is correct.