Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29

Step-by-step explanation:

Hello,

I assume that we are working in , otherwise there is only one zero which is 1. Please consider the following.

First of all, we can notice that 1 is a trivial solution as

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

Now, we need to find the zeroes of the second factor, meaning finding x so that:

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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