Which of the following functions best represents the graph?

f(x) = x3 + x2 − 4x − 4
f(x) = x3 + 4x2 − x − 4
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 4x − 8

Step-by-step explanation:

From the graph, the x-intercepts are;

These are root of the polynomial function represented by the given graph.

By the remainder theorem;

According to the factor theorem, if is a factor of , then

This implies that;

are factors of the required function.

Hence;

We expand using difference of two squares to obtain;

We expand using the distributive property to get;

Rewrite in standard form to obtain;

Choice A: f(x) = x^3 + x^2 − 4x − 4

Step-by-step explanation:

Here's a great and simple answer.

Ok first we need to take the x intercepts to solve.

If we look at the graph we see the x ints are -2,+1 and +2.

To solve we need to put them into factor form

= (x-2) (x+2) and (x+1)

Simplify: (x-2) (x+2) = (x^2-4) and (x+1)

Now we take (x^2-4) and (x+1) and multiply them to find our answer

(x^2-4) (x+1)

= x^2(x) and x^2(1) = x^3 and x^2.

now the other: -4(x) and -4(+1) = -4x and -4

We have nothing common here so we just join them

= x^3 + x^2 - 4x - 4, and that is the same as choice A.

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