Determine the value of a if x-2 is a factor of x^3 - ax^2 + 17x-50

Answer 1

Just plug x=2 into the cubic equation to get

8-4a +34 -50 =

-8 -4a

set it =0

-8-4a =0

4a = -8

a = -2

x-2 is a factor of x^3 +2x^2 +17x -50. the other factor is x^2 + 4x + 25

(x-2)(x^2+4x+25) = x^3 +2x^2 +17x -50

x^2 +4x + 25 has no real factors. set it equal to zero, solve for x, you get imaginary zeroes and imaginary factors.

Answer 2

Using synthetic division you would have

2 1 a -17 50

2 4+2a -26+4a

1 2+a -13+2a 24+4a

For x-2 to be a factor 24 + 4a = 0

This gives 4a = -24

a = -6