1. ## [SOLVED] Miscellaneous Factors

Q. Factorise the following:

$\displaystyle z^3 - 7z - z^2 + 7$
had a look at the answer and is $\displaystyle (z - 1)(z^2 - 7)$
i tried the group in pairs method but i didn't get the answer, and now i have no idea on how to work it out.
if anyone can show me the full working out that would be a great help, thanks

2. Originally Posted by waven
Q. Factorise the following:

$\displaystyle z^3 - 7z - z^2 + 7$
had a look at the answer and is $\displaystyle (z - 1)(z^2 - 7)$
i tried the group in pairs method but i didn't get the answer, and now i have no idea on how to work it out.
if anyone can show me the full working out that would be a great help, thanks
It can be written as

z^3-z^2 -7z + 7

1z^2*(z-1) -7*(z-1)

Take (z-1) out as common

2 (z^2-7)*(z-1)

Tell the step number where you had/have trouble

$\displaystyle z^3 - 7z - z^2 + 7$
had a look at the answer and is $\displaystyle (z - 1)(z^2 - 7)$
Let $\displaystyle p(z) = z^3 - 7z - z^2 + 7$. By inspection, p(1) = 0. Therefore (z - 1) is a factor of $\displaystyle z^3 - 7z - z^2 + 7$. Divide (z - 1) into the cubic to get the quadratic factor.