Question

Show That x^2-1 is divisible by x-1 and find the other factor​

Answer 1

Answer:

x^2-1=(x-1)(x+1). so it's divisible by x-1 and other factor is x+1

Answer 2

Answer:

x²-1 = x² - 1²

a² - b² = (a+b)(a-b)

=> x² - 1² = (x+1)(x-1)

Since (x-1) is a factor of x² - 1, it is completely divisible.

To recheck;

p(x) = x² - 1

p(1) = 1² - 1 [Remainder Theorem]

p(1) = 0 [Factor Theorem]

The other factor is (x+1)