Solving Polynomial Equations

This worksheet focuses on solving polynomial equations using various algebraic techniques appropriate for Grade 12 mathematics.

Grade 12 Math AlgebraSolving Polynomial Equations

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Includes

2 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

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

Topics

polynomialsalgebraequationsgrade 12

7 sections · Free to use · Printable

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Date:

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Read each question carefully and solve the polynomial equations using the most appropriate method. Show all your work for full credit.

1. Solve the polynomial equation by factoring: x³ - 4x² - 5x = 0

2. Find all real roots of the equation: 2x³ + 7x² + 6x = 0

3. Which of the following is a possible rational root of the polynomial P(x) = 3x³ - 2x² + 5x - 6?

-1/2

2/3

5/3

4. If (x - 2) is a factor of P(x) = x³ - 3x² + kx - 2, then the value of k is .

5. Use synthetic division to find the quotient and remainder when (x⁴ - 5x² + 4) is divided by (x + 2). The quotient is and the remainder is .

6. Find all complex roots of the equation: x³ + 8 = 0

7. Given that 2 is a root of x⁴ - 2x³ - 7x² + 8x + 12 = 0, find all other roots.

8. A polynomial of degree 'n' always has 'n' real roots.

True

False

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