SOLUTION: given the polynomial P(x)=x^4-2x^3-7x^2+18x-18 a. without long division, find the remainder if P is divided by x+1 b. if one zero of P is 1-i, find the remaining zeros of P c. w

a) Use synthetic division:

For the divisor, the form is x-a, so for x+1 we have a=-1:



 -1 | 1  -2  -7  18  -18

    |    -1   3   4  -22

    |____________________

      1  -3  -4  22  -40    --> Remainder is -40



b) If  x=1-i  is a root, then too must be x=1+i as complex roots always come in conjugate pairs.    ... and now we can divide:



     --> x=-3 and x=3 are also zeros



c)  Part (b) has the four factors, using real valued polynomials: