Write an equation for each polynomial given a Degree 6 has r

Write an equation for each polynomial, given...

(a) Degree 6, has roots at x = 1, 2, 3, 6.

(b) Odd degree, has 2 distinct roots.

(d) Has a double root at x = 1 and a triple root at x = 5. Passes through the point (1, 16)

Degree 6, has roots at x = 1, 2, 3, 6.

Lets simply consider = 1 to have multiplicity of 3

So, itd be :

(x-1)^3 * (x - 2)(x - 3)(x - 6)

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(b) Odd degree, has 2 distinct roots.

This could be :

y = (x - 1)^2 * (x + 2)

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This will be of the form :

y = a(x + 3)^3 * (x - 3)

Now, plug in (0,27) to find constant a :
27 = a(3)^3(-3)

a = -1/3

So, we have :

y = -1/3 * (x + 3)^3 * (x - 3)

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d) Has a double root at x = 1 and a triple root at x = 5. Passes through the point (1, 16)

y = a* (x + 1)^2 * (x - 5)^3

Using (1,-16) :
-16 = a * (4) * (-64

a = 1/16

So, y = 1/16 * (x + 1)^2 * (x - 5)^3