Cubic Equations Worksheet

A Grade 11 math worksheet focused on solving and understanding cubic equations, including factoring, rational root theorem, and graphing.

Grade 11 Math AlgebraCubic Equations

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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.APR.B.2CCSS.MATH.CONTENT.HSA.APR.B.3

Topics

cubic equationsalgebragrade 11math

8 sections · Free to use · Printable

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Factor the following cubic equation completely: x³ - 6x² + 11x - 6 = 0

2. According to the Rational Root Theorem, the possible rational roots of the polynomial P(x) = 2x³ + 3x² - 8x + 3 are .

3. If x = 1 is a root of the equation x³ + kx² - 7x + 3 = 0, then the value of k is .

4. Which of the following is a root of the equation x³ - 2x² - 5x + 6 = 0?

x = 1

x = 0

x = -1

x = 2

5. Consider the cubic function f(x) = x³ - x. Sketch the graph of this function, clearly indicating its x-intercepts and y-intercept.

6. A cubic equation always has exactly three real roots.

True

False

7. Find all roots (real and complex) of the equation x³ - 8 = 0.