Question

Find a polynomial f(x) of degree 4 that has the following zeros.
0, -4, (multiplicity ), 2
Leave your answer in factored form.

Answer 1

Answer:

$f(x)=(x-2)(x)(x+4)^2$

Step-by-step explanation:

Since there is a multiplicity at x=-4, that would meant that that part of the factor would have to have an even degree. This means that it would have to be 2.

This would give you $f(x)=(x-2)(x)(x+4)^2$

Answer 2

Answer:

$f (x) = x (x + 4)^2(x-2)$

Step-by-step explanation:

The zeros of the polynomial are all the values of x for which the function $f (x) = 0$

In this case we know that the zeros are:

$x = -4,\ x+4 =0$

$x = -4,\ x+4 =0$

$x = 0$

$x = 2$, $x - 2 = 0$

Now we can write the polynomial as a product of its factors

$f (x) = x (x + 4)(x+4) (x-2)$

$f (x) = x (x + 4)^2(x-2)$

Note that the polynomial is of degree 4 because the greatest exponent of the variable x that results from multiplying the factors of f(x) is 4