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Ivan
2 years ago
8

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

Mathematics
1 answer:
Marysya12 [62]2 years ago
6 0

Answer:

a=12

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

_______<u> -3</u>

      2      | 0

-3 | 2 a 19 3

_______<u> -3</u>

      2    1 | 0

-3 | 2 a 19 3

_____<u>-18 -3</u>

     2     1 | 0

-3 | 2 a 19 3

_____<u> -18 -3</u>

     2  6  1 | 0

-3 | 2 a 19 3

_____<u> -18 -3</u>

     2  6  1 | 0

-3 | 2 a 19 3

____<u>-6 -18 -3</u>

     2  6  1 | 0

a - 6 = 6

a = 12

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