Question

Which polynomial function has a leading coefficient of 1 and roots 21 and 31 with multiplicity 1?

f(x) = (x - 2)(x – 31)

f(x) = (x + 21)(x + 3)

f(x) = (x - 2)(x − 3)(x - 2)(x – 31)

fix) = (x + 2y + 211

Answer 1

Which i think is the first one, there may just be a typing error.

Explanation:

A polynomial of order n has the following format:

`f(x) = a(x - x_(0))(x - x_(1))...(x - x_(n-1))`

In which a is the leading coefficient,
`x_(0), x_(1),..., x_(n-1)` are the roots.

If a root appears m times, they are said to have multiplicity m.

Leading coefficient of 1 and roots 21 and 31 with multiplicity 1

`f(x) = 1(x - 21)(x - 31)`

So the correct answer is:

`f(x) = 1(x - 21)(x - 31)`

Which i think is the first one, there may just be a typing error.