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