Question

If x − 2 is a factor of the following two polynomials, find the values of a in each case x⁵ − 3x⁴ − ax³ + 3ax² + 2ax + 4.

Answer 1

 Let f(x) = x⁵ − 3x⁴ − ax³ + 3ax² + 2ax + 4 be the given polynomial.

By the factor theorem, (x − 2) is a factor of f(x), if f (2) = 0

Therefore,

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

                                                     `32 - 48 - 8a + 12a + 4a + 4 = 0`

` - 12 + 8a = 0`

` a = 3/2`

Thus, the value of a is 3/2.