Help with Finding Zeros

[coolcat125]

Hi everyone! I have pre-calculus homework and I'm currently stuck on this one question: "Using the given zero, find all of the zeros and write a linear factorization of f(x). The given function and zero is 1+i and f(x) = x⁴-2x³-x²+6x-6
I began this question by synthetically dividing f(x) by the given zero, which we were taught in class to do. However, I am now stuck with the quotient: x³-1+ix²-3x+3-3i

How do I find the rest of the zeros with this? Thank you!

 

[Romsek]

f(x) has real coefficients. What does that tell you about any complex roots?

 

[Steven G]

You should do long division dividing by a quadratic using the hint by Romsek.

 

[coolcat125]

f(x) has real coefficients. What does that tell you about any complex roots?

You should do long division dividing by a quadratic using the hint by Romsek.

Thanks everyone for your help, I got the answer!

 

[HallsofIvy]

I find x³-1+ix²-3x+3-3i confusing- particularly that "-1".

Do you mean x³- (1+i)x²-3x+3-3i ?