Grade 9 Cubic Equations Worksheet
Explore and solve cubic equations with this comprehensive worksheet for Grade 9 students, covering factoring, roots, and graphical analysis.
Includes
Standards
Cubic Equations Worksheet
Name:
Date:
Score:
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?
Related Worksheets
Rationalizing Radicals Worksheet
Grade 9 Math worksheet focusing on rationalizing single and binomial denominator radicals.
Solving Square Root Equations
Practice solving square root equations with various levels of complexity. This worksheet covers isolating the radical, squaring both sides, and checking for extraneous solutions.
Zero Product Property Worksheet
Practice solving quadratic equations using the Zero Product Property for Grade 9 algebra.
Simplifying Polynomials Worksheet
Grade 9 Math worksheet focusing on simplifying polynomials through addition, subtraction, and multiplication.
Pascal's Triangle Worksheet
Explore the patterns and properties of Pascal's Triangle, including its construction, binomial coefficients, and relationships to other mathematical concepts.
Solving Three-Step Equations
This worksheet provides practice for grade 9 students in solving linear equations that require three steps.
Elimination Method Worksheet
Practice solving systems of linear equations using the elimination method for Grade 9 students.
Rearranging Equations Worksheet
A Grade 9 math worksheet focusing on rearranging algebraic equations to solve for different variables.