Answer:
Error of Andrew: Made incorrect factors from the roots
Step-by-step explanation:
Roots of the polynomial are: 3, 2 + 2i, 2 - 2i. According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is a factor of P(x). According to this definition:
(x - 3) , (x - (2 + 2i)) , (x - (2 - 2i)) are factors of the required polynomial.
Simplifying the brackets, we get:
(x - 3), (x - 2 - 2i), (x - 2 + 2i) are factors of the required polynomial.
This is the step where Andrew made the error. The factors will always be of the form (x - a) , not (x + a). Andrew wrote the complex factors in form of (x + a) which resulted in the wrong answer.
So, the polynomial would be:
We have the function and we want to find a function that has the same y-intercept than the previous function.
First, let's find the y-intercept by subtituting 0 for 'x'.
Now that we found that y-intercept =-3, any lineal function of the type: will have the same y-intercept. Where 'a' can take all the real values.
Also, any quadratic function of the type: will have the same y-intercept. Where 'a' and 'b' can take all the real values.