Question

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Which polynomial function has a leading coefficient of 2, root –4 with multiplicity 3, and root 10 with multiplicity 1?
a)f(x) = 2(x – 4)(x – 4)(x – 4)(x + 10)
b) f(x) = 2(x + 4)(x + 4)(x + 4)(x – 10)
c)f(x) = 3(x – 4)(x – 4)(x + 10)
d)f(x) = 3(x + 4)(x + 4)(x – 10)

Answer 1

The answer here is B.

This is because the leading coefficient is 2, as 2 is the first number in the function. We can immediately rule out C and D for this also.

If a root is negative, the factor will have an addition symbol inside. Since your root is -4, the factor will be (x + 4). Since (x + 4) is shown 3 times, it has a multiplicity of 3. We can rule out B for this, since the root would be +4 instead of -4.

Using the same root/factor rule (root and factor have opposite signs), B would be the right answer also because the root is +10 (the factor is x - 10) and is shown once (multiplicity of 1).

Answer 2

answer:

B

hope this helps! :o)