3. Use the given information about the polynomial graph to write out the equation. Degree 5, Roots of multiplicity 2 at x = 3 and x = -2 and a root of multiplicity 1 at x = 4,
y-intercept at (0,12).

Step-by-step explanation:

The standard form for a polynomial equation in its factored form is:

Where p and q are the zeros and a is the leading coefficient.

We know that the degree of the polynomial is 5.

We are also given roots at x=3 and x=-2. Hence, our factors are (x-3) and (x+2).

These have a multiplicity of two, so we will square them.

We also know that there is a root at x=4. Hence, the factor is (x-4). This has a multiplicity of 1.

Therefore, our polynomial is now:

We know that the y-intercept is 12. Therefore, if we substitute in 0 for x, we should get 12 for y. Here, we are solving for our a. Therefore:

Evaluate:

Evaluate:

Divide both sides by -144:

Hence, our entire polynomial is:

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24

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