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Find the Value of A, If X – 2 is a Factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8. - ICSE Class 10 - Mathematics

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Question

Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8. 

Solution

f(x) = 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8
x – 2 = 0 ⇒  x = 2
Since, x – 2 is a factor of f(x), remainder = 0.
2(2)5 – 6(2)4 – 2a(2)3 + 6a(2)2 + 4a(2) + 8 = 0
64 – 96 – 16a + 24a + 8a + 8 = 0
-24 + 16a = 0
16a = 24
a = 1.5

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Solution Find the Value of A, If X – 2 is a Factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8. Concept: Factor Theorem.
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