Use synthetic division to determine if the given value for k is a zero of this polynomial. If not, determine p(k).

Question

Use synthetic division to determine if the given value for  is a zero of this polynomial. If not, determine p(k).

p(x)=3x^2−(5−5i)x+(28−20i);k=−4i

Answer 1

The synthetic division process is to bring down the coefficient of the highest term and to then multiply with the divisor and add to next higher term and continue until you get to the constant term. It will look something like:

-4i 3 - 5 +5i 28 - 20i

-12i -28 + 20i

3 5 - 7i 0

The 0 remainder means k = -4i is a zero of the polynomial