Given:
There are given that the zeroes and degrees of the polynomial:
Explanation:
From the concept of a polynomial:
A polynomial has a as zero if and only if (x -a) is a factor of the polynomial.
Then,
From the given polynomial:
Then,
Final answer:
Hence, the polynomial is shown below:
Recall the polynomial remainder theorem: if is a factor of some polynomial
, then the remainder upon dividing
by
is
.
Let and
. The remainder left from dividing
by
is
If we subtract 5 from both sides, we'd get a "remainder" of 0, which suggests that we have to add -5 to to make
a factor.