Question

Determine the unknown coefficient a, if x + 3 is a factor of f(x) = 2x^3 + ax^2+ 19x + 3

Answer 1

`a=12`

Explanation:

Work backwards with synthetic division with remainder 0 and then solve for a:

-3 | 2 a 19 3

_________

2 | 0

-3 | 2 a 19 3

_______ -3

2 | 0

-3 | 2 a 19 3

_______ -3

2 1 | 0

-3 | 2 a 19 3

_____-18 -3

2 1 | 0

-3 | 2 a 19 3

_____ -18 -3

2 6 1 | 0

-3 | 2 a 19 3

_____ -18 -3

2 6 1 | 0

-3 | 2 a 19 3

____-6 -18 -3

2 6 1 | 0

a - 6 = 6

a = 12