Pls answer?

Question

1. Use the remainder theorem and find the remainder when P(x)=x^4-5x^3+4x-4 is divided by x+2?
2.Determine the values of K for which 3x^@+KX+12=0 has exactly one solution?
3. Write a quadratic function with -3+5i and -3-5 as the solutions.
4. SOlve x^2+2x+3>11.Graph the solution set on a number line.

Answer 1

1. The quotient is x^3 - 7x^2 + 14x - 24 and the remainder is 44.

2. There is exactly one solution when the discriminant b^2 - 4ac =0. Here a = 3, b = k, and c = 12, and the discriminant is k^2 - 144. This = 0 when k = +-12.

3. In factored form the function is [x - (-3 + 5i)][x - (-3 - 5i)]. You can do the multiplication.

4. x^2 + 2x + 3 > 11 if and only if x^2 + 2x - 8 > 0. The graph of f(x) = x^2 + 2x - 8 is a parabola which opens up, and f(x) > 0 when x is not between the roots of f(x) = 0. Since f(x) = 0 at x = -4 and x = 2, we have f(x) > 0 when x < -4 or x > 2.