Question

1. Which expression is a cubic polynomial?

3x^2 - 1
x^3 - 1
x^2 - x + 3
3x^2 - x + 3

2.Which of the following binomials is a factor of x^3 + 4x^2 +x - 6?

3. If a polynomial equation p(x) = 0 has 3 + 4i as a solution, what other solutions must it have?

Answer 1

1. x^3 - 1

2. P(x) = (x + 5)(x + 2)(x)

3. x + 2

4. 3 - 4i

Explanation:

Answer 2

1. A cubic polynomial is a polynomial of degree 3 (the degree of a polynomial is the highest degree among al terms), then the cubic polynomial is
`x^3- 1`.

2. The polynomial
`x^3 + 4x^2 +x - 6` has root x=1, then
`x^3 + 4x^2 +x - 6=(x-1)(x^2+5x+6)=(x-1)(x+2)(x+3)`.

3. If a polynomial equation p(x) = 0 has 3 + 4i as a solution and has real coefficients, then 3-4i is also a solution.