Maths Q's Polynomials (1 Viewer)

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x.Exhaust.x

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1. Consider the cubic expression p[x] = ax^3 + bx^2 + cx + d
a) Given that p[x] is an odd function, evaluate b and d
b) It is now given that p[x] is monic. What conditions must exist on c for 3 real roots?

2. Factorise f(x)=x^6-x^5-17x^4+5x^3+64x^2-4x-48

So far I've got factors of 1, 2, -2, -3, 4 which all amount to 0 (remainder theorem). Now my mind is blank as to what to continue on with.

3. Consiver the cubic polynomial p(x) = ax^3 + bx^2 + cx + d

a) Show that p(x)-p(alpha)= (x-alpha).q(x) for some q(x)

b) Deduce the remainder theorem for a cubic polynomial.

Thanks in advance.
 
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