Grade 9 Cubic Equations Worksheet
Explore and solve cubic equations with this comprehensive worksheet for Grade 9 students, covering factoring, roots, and graphical analysis.
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Cubic Equations Worksheet
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Read each question carefully and provide the best possible answer. Show all your work for full credit.
1. Which of the following is a cubic equation?
$$2x^2 + 3x - 1 = 0$$
$$4x^3 - 5x + 2 = 0$$
$$x^4 + 2x^2 - 7 = 0$$
$$5x - 8 = 0$$
2. How many real roots can a cubic equation have?
Exactly one
Exactly two
One, two, or three
At most four
3. The general form of a cubic equation is ax³ + bx² + cx + d = 0, where 'a' cannot be .
4. A cubic equation will always have at least one root.
5. The graph of a cubic function is also known as a curve.
6. Factor the cubic expression: $$x^3 - 8$$
7. Find the real root(s) of the equation: $$x^3 + 2x^2 - x - 2 = 0$$
8. All cubic equations have three distinct real roots.
True
False
9. If $(x-k)$ is a factor of a cubic polynomial, then $k$ is a root of the polynomial.
True
False
10. Consider the cubic function $$f(x) = x^3 - 3x^2 - x + 3$$
a) Plot the function on the graph below. (Hint: Find the roots first.)
b) What are the x-intercepts of the function?