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: 

  



  

RELATED QUESTIONS

given the polynomial p(x) = x^4-2x^3-7x^2+18-18

If one zero of P is 1-i, find the... (answered by Seutip)

If P(x) =3x to the 3rd power + 7x squared - 2x +6, use the remainder theorem to find the... (answered by RAY100)

A polynomial P(x) and a divisor d(x) are given. Use long division to find the
quotient... (answered by Jk22)

a Polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient... (answered by KMST)

when the polynomial p(x) is divided by (x-2) the remainder is 4 and when p(x) is divided... (answered by JThomson)

find the remainder if p(x)=2x^3-5x^2+9x-3 is divided by... (answered by jim_thompson5910)

Could someone please help?

Use synthetic division and the Remainder Theorem to find... (answered by stanbon)

Determine whether the polynomial P(x) has a zero remainder when divided by  (x-3).... (answered by stanbon)

Hello.  My question is When a polynomial P(x) is divided by 2x+1, the quotient is... (answered by Edwin McCravy)