SOLUTION: Please help me solve the following questions. Question1. If (x-k) is a factor of the polynomial f(x) = 4x3 � (3k + 2)x2 � (k2 - 1)x + 3, where k is a constant, find the poss

Question 135335: Please help me solve the following questions.
Question1.
If (x-k) is a factor of the polynomial f(x) = 4x3 � (3k + 2)x2 � (k2 - 1)x + 3, where k is a constant, find the possible values of k.
Question2.
A polynomial p(x) is of the form p(x) = ax2 + bx + c , where a, b, c, m, and k are mx + k constants. If the truth set of p(x) = 0 is {1, 2} find the values of a, b and c.
Question3.
Find all the possible solutions of x in the equation x3 + 27 = 0, where x is a complex number.
Question5.
7. (i) Given the complex numbers z1 = 3i; z2 = 2 + 4i; z3 = 5 � 3i.
Express z1z2 + z2z3 + z3z1 , in the form x + iy where x and y are real numbers.
z1 + z2 + z3
(ii) Given that cos5Ө + isinӨ equals (cos5Ө + isinӨ)5, show that
sin5Ө = 16cos4Ө - 12cos2Ө + 1, where Ө is real and is not an integral multiples of π.
sinӨ

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Use synthetic division. At the end, you get k - 2k^2 and 3 ... These must sum to zero for x - k to be a factor.
3 + k - 2k^2 = 0
(3 - 2k)(1 + k) = 0
3 - 2k = 0 and 1 + k = 0
3/2 = k and k = -1
You would have to explain question (2) better.
x^3 = -27
x = -3 .. no complex values unless 0i - 3
Just multiply those out for (5)
I think Euler's equation might help for (ii) or the precalc version. It's been a long time since that.
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