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Probability of head: p= 1/2 and hence the probability of tail, q =1/2. For exactly two heads: x=2. P (x=2) = 5 C2 p 2 q 5-2 = 5! / 2! 3! × (½) 2 × (½) 3. P (x=2) = 5/16. (b) For at least four heads, Deduce that if f is irreducible (over some field), then this happens iff f ′ = 0, and thus over a field of characteristic p > 0 this can happen iff all the non-zero coefficients of f correspond …
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Here a general dis-The polynomial p (x) = 0 is called the zero polynomial. ... p (x) = d (x) q (x) + r (x). The key idea in performing the division is to keep working with the leading terms, as the following example shows. ... Consider the polynomial p (x) = a n x n − a n − 1 x n − 1 + ... + a 1 x + a 0, where all the coefficients are integers. Suppose that ...The Roots - "Stomp" (Feat. P.O.R.N.) Video. The Roots are rolling out a new video and track from their upcoming concept LP undun each Tuesday and this week's edition comes in the form of ...m2(P m(R))0by ' j(p) = p(j)(5) j!: So suppose a 0;:::;a m2F and a 0 + a 1(x 5) + :::+ a m(x 5)m= 0: Then for j= 0;1;:::;m, we have a j= ' j(a 0 + a 1(x 5) + :::+ a m(x 5)m) = ' j(0) = 0. Thus a 0 = a 1 = :::= a m= 0. Hence 1;x 5;:::;(x 5)mis a linearly independent list in P m(R) of length m+ 1, which equals the dimension of P m(R). 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