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Question 20
If x + 2a is a factor of x54a2x3+2x+2a+3, then find the value of a.

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Solution

Let p(x)=x54a2x3+2x+2a+3
Since x + 2a is a factor of p(x), p (-2a) = 0 [Using Remainder Theorem].
(2a)54a2(2a)3+2(2a)+2a+3=0
32a5+32a54a+2a+3=0
2a+3=0
2a3=0
a=32
Hence, the value of a is 32.

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