Question

In the following two polynomials, find the value of a, if x − a is  factor x⁶ − ax⁵ + x⁴ − ax³ + 3x − a + 2.

Answer 1

 Let  `f(x) = x^6 - ax^5 + x^4 - ax^3 + 3x - a + 2` be the given polynomial.

By factor theorem, (x − a) is a factor of the polynomial if f(a) = 0

Therefore,

`f(a) = a^6 -a(a)^5 + (a)^4 + (a)^4 - a(a)^3 + 3(a) - a + 2 = 0`

`a^6 - a^6 + 4^4 - a^4 + 2a + 2 = 0`

                                     `2a + 2 = 0`

                                               `a=-1`

Thus, the value of a is − 1.