Form a polynomial whose zeros and degree are given. Zeros: −3, 3, 2; degree: 3 Type a polynomial with integer coefficients and a leading coefficient of 1
Accepted Solution
A:
If a polynomial P(x) has a zero equal to a, then (x-a) is a factor of this polynomial. So if a polynomial has zeros a, b and c then it has we could write:
P(x)=(x-a)(x-b)(x-c).
Here we can clearly see that a, making the left hand side 0 because of the factor (x-a), makes the left hand side 0 as well. This means that P(a)=0. This illustrates the discussion above.
Thus, substituting a, b, c with −3, 3, 2 we can write P(x)=(x+3)(x-3)(x-2).
We can expand the right hand side to have the polynomial in standard form: