Question 1169758
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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.   {{{ (x-1+i)(x-1-i) = x^2+(-1-i)x+(-1+i)x + (-1+i)(-1-i) = 
x^2-2x+2 }}} ... and now we can divide:

    {{{ (x^4-2x^3-7x^2+18x-18) / (x^2-2x+2) = x^2-9 }}} --> x=-3 and x=3 are also zeros

c)  Part (b) has the four factors, using real valued polynomials: 
{{{ P(x) = (x+3)(x-3)(x^2-2x+2) }}}