SOLUTION: Factorise each of the following over C a) f(z)=z^3+z^2+2z-4 b)g(z)= z^3+(2-i)z^2-z-2+i i tried solving them as: a) the factor of f(z) is (z-1), then do the long division and

Algebra ->  Trigonometry-basics -> SOLUTION: Factorise each of the following over C a) f(z)=z^3+z^2+2z-4 b)g(z)= z^3+(2-i)z^2-z-2+i i tried solving them as: a) the factor of f(z) is (z-1), then do the long division and       Log On


   



Question 470838: Factorise each of the following over C
a) f(z)=z^3+z^2+2z-4
b)g(z)= z^3+(2-i)z^2-z-2+i
i tried solving them as:
a) the factor of f(z) is (z-1), then do the long division and the answer will be (z^2+2z+4) and so
f(z)=(z-1)(z^2+2z+4)
= (z-1)(z+1)^2 -1+4 <<< got stuck, how can i complete?
b)the factor of g(z) is (z+2+i), then do the long division and the answer will be z^2+1 and so
g(z)= (z+2-i)(z^2-1) <<<< how can i complete?
Thanks

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

On problem number 1, so far, so good.



Just like you said. Next take the quadratic factor and set it equal to zero, then solve the quadratic equation using the quadratic formula:

.

Hence the factors of the quadratic trinomial are:



Hence:



The other one is easier. Factor the quadratic factor as the difference of two squares.

John

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