thanks for the help, i understood it well. if you could can you also help me in these three questions as I am not understanding how to do them.Or doing the usual way:
You can then do a rough sketch of this cubic polynomial and read off the positive intervals.
Could you please explain question 1 further as I am not quite understanding what you mean.1. if (x-1) divides the polynomial, and it divides (x^2-1)Q(x), it must divide the remainder (kx+2). Thus you can figure out k. Then, using this, divide the polynomial by (x+1). Since (x+1) already divides (x^2-1)Q(x), the remainder is found when (kx+2) is divided by (x+1)
2. Using the remainder theorem, the remainder when divided by (x-1) is equivalent to P(1), since if P(x)=(x-1)Q(x) + k, P(1) = k. Similarly, dividing by x gives the remainder P(0). this should give u the equation to find k.
3. Using the relationship between roots and coefficients, find b c and d in terms of a and k. Sub into equation to show it equals 0.