Question

find the value of a if x minus A is a factor of x cube minus x square - 2 X + a - 1

Answer 1

your question is ---> find value of a , if (x - a) is a factor of x³ - x² - 2x + a + 1.

given, (x - a) is a factor of x³ - x² - 2x + a - 1,

or, x = a is a root of x³ - x² - 2x + a + 1

we know, if f(x) is a polynomial and a is a root of this polynomial.then, f(a) = 0.

so, (a)³ - (a)² - 2(a) + a + 1 = 0

or, a³ - a² - 2a + a + 1 = 0

or, a³ - a² - a + 1 = 0

or, a²(a - 1) - 1(a - 1) = 0

or, (a² - 1)(a - 1) = 0

or, (a - 1)(a + 1)(a - 1) = 0

or, a = 1 or -1

hence, value of a = 1 or -1.

Answer 2

Answer:

hope it helps you