Explanation:
the multiplication of multiple factors is zero, if at least one factor is zero.
and to get a polynomial of degree 4 (that means there is a term of x⁴) we need 4 factors each a term in x. so, x×x×x×x = x⁴.
it is nice to get all 4 zeros defined. these zeroes mean that f(x) = 0 for x = -7, x = 0, x = 2 and x = 3.
how do we make sure that is the case ?
by defining corresponding factors for f(x).
f(x) = (x + 7)x(x - 2)(x - 3)
that function is 0 for x = -7, x = 0, x = 2, x = 3.
done.