The degree of h(x) is 6.
You can find this answer by determining what the factors of the factored form of the polynomial are. The problem states that each zero will have a multiplicity of one. So we can start with the first zero the problem talks about:
x=3-4i
in order to find this first factor, we can go ahead and set that equation equal to zero. The left side you end up with will be our first factor.
x-3+4i=0
therefore the first factor is (x-3+4i)
Now, whenever we are talking about complex zeros, they will come in pairs. This is because the number that contains the i can either be positive or negative, therefore the next zero will be:
x=3+4i
when setting this equation equal to zero, we get:
x-3-4i=0 so the second factor is (x-3-4i)
Now, we can find the zeros on the given table. These are the x-values where h(x)=0. So, the next zero will be:
x=-5, so x+5=0, the next factor is: (x+5)
next,
x=-1, so x+1=0, the next factor is: (x+1)
next,
x=4, so x-4=0, the next factor is: (x-4)
next,
x=10, so x-10=0, the next factor is: (x-10)
so that will be all our zeros, so the function looks like this:
h(x)=k(x-3+4i)(x-3-4i)(x+5)(x+1)(x-4)(x-10)
Notice we have 6 factors with a multiplicity of 1 each, after multiplying all of them together, our first term would be an [tex]x^{6}[/tex] so the degree of the polynomial is a 6.
For further information take a look at the following question.
https://brainly.com/question/18149644?referrer=searchResults
