Question

Which polynomial function has a leading coefficient of 1, roots –3 and 8 with multiplicity 1, and root 4 with multiplicity 2?

f(x) = 2(x + 3)(x + 4)(x – 3)
f(x) = 2(x – 8)(x – 4)(x + 3)
f(x) = (x + 8)(x + 4)(x + 4)(x – 3)
f(x) = (x – 8)(x – 4)(x – 4)(x + 3)

Answer 1

f(x) = (x-8)(x-4)(x-4)(x+3)

Answer 2

Answer:

f(x) = (x – 8)(x – 4)(x – 4)(x + 3)

Step-by-step explanation:

A polynomial function with roots $x_{1}, x_{2}, ..., x_{n}$ has the following format:

$f(x) = a(x - x_{1})(x - x_{2})...(x - x_{n})$

In which a is the leading coefficient.

In this problem, we have that:

Leading coefficient 1, so $a = 1$

roots -3 and 8 with multiplicity 1, so $(x + 3)(x - 8)$.

root 4 with multiplicity 2, so $(x - 4)^{2} = (x - 4)(x - 4)$

So the correct answer is:

f(x) = (x – 8)(x – 4)(x – 4)(x + 3)