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

Determine The Unknown Coefficient A If X 3 Is A Factor Of Fx 2x3 Ax2 19x 3 class=

Sagot :

Answer:

[tex]a=12[/tex]

Step-by-step 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

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