u) 2y + 1 Is a TDCI UI LY
(iv) 2x - 3 is factor of x + 2x3 - 9x2 + 12
Show that p-- 1 is a factor of p10 - 1 and also of p11 - 1.
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Let g (p) = p10 -1
and h(p) = p11 -1.
On putting p=1 in Eq. (i), we get
g(1)=110-1= 1-1=0 Hence, p-1 is a factor of g(p).
Again, putting p = 1 in Eq. (ii), we get
h (1) = (1)11 -1 = 1 -1 = 0 Hence, p -1 is a factor of h(p).
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