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Question 21
Find the value of m, so the 2x- 1 be a factor of 8x4+4x316x2+10x+m.

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Solution

Let p(x)=8x4+4x316x2+10x+m.
Since 2x - 1 is a factor of p(x), P(12)=0[Using Remainder Theorem]
8(12)4+4(12)316(12)2+10(12)+m=0
8×116+4×1816×14+10(12)+m=0
12+124+5+m=0
1+1+m=0
m=2

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