Question

(z-1) is a factor of z³-1.
true or false
​

Answer 1

Answer:

• true

Step-by-step explanation:

z³-1= z³-1³ =(z-1)(z²+1+z)

Answer 2

Answer:

True

Step-by-step explanation:

$divding \: \: z {}^{3} - 1 \: by \: z - 1 \\ let \: (z {}^{3} - 1) \: be \: p(z) \\ \\by \: factor \: theorem \\ (z - 1) \: will \: be \: a \: factor \: of \: p(x) \: if \: p(1) = 0 \\ p(z) = z {}^{3} - 1 \\ p(1) = 1 {}^{3} - 1 \\ p (1) = 1 - 1 \\ p(1) = 0 \\ \\ hence \: it \: is \: a \: factor \: of \: z {}^{3} - 1$

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