Question

Using factor theorem show x – 2 is a factor of x^6 – 64

Answer 1

f(x) = f(2)

x = 2

Putting the value of x in given equation :

x^6 – 64

(2)^6 – 64

64 - 64

0

As the remainder is 0, (x – 2) is the factor of given equation by factor theorem

Answer 2

Let see your answer !!!!!

$let \: p(x) = x ^{6} - 64 \\ \\ f(x) = x - 2 \\ \\ = > 0 = x - 2 \\ \\ = > 2 = x \\ \\ = > x = 2 \\ \\ by \: factor \: theorem \\ \\ p(2) = (2) ^{6} - 64 \\ \\ = 64 - 64 \\ \\ = 0$


Since remainder is 0. So , f(x) is the factor of p(x).




Thanks :)))))