Polynomial Division Worksheet
Grade 12 math worksheet on dividing polynomials using synthetic and long division, including questions with remainders and missing terms.
Includes
Standards
Polynomial Division
Name:
Date:
Score:
Read each question carefully and show all your work. Use synthetic division where appropriate, otherwise use long division.
1. Divide (x³ + 2x² - 5x + 12) by (x - 2).
2. Perform synthetic division to find the quotient and remainder of (2x⁴ - 3x² + 5x - 1) ÷ (x + 1).
3. Use long division to divide (3x³ - 4x² + 7x - 5) by (x² + x - 1).
4. Find the quotient and remainder when (x⁴ - 2x³ + 5x² - 8x + 4) is divided by (x - 3).
5. When dividing a polynomial P(x) by (x - c), if the remainder is 0, then (x - c) is a of P(x).
6. Synthetic division can only be used when the divisor is a linear factor of the form .
7. What is the remainder when (x⁵ - 3x⁴ + 2x² - 7) is divided by (x - 1)?
-7
-5
0
1
8. If (x + 2) is a factor of P(x) = x³ + kx² - 4x + 12, find the value of k.
Related Worksheets
Perfect Square Trinomials
This worksheet focuses on identifying, factoring, and constructing perfect square trinomials, essential skills for Grade 12 Algebra.
Equations with Infinite and No Solutions
Explore linear equations that result in infinite solutions (identities) or no solutions (contradictions) at a Grade 12 level.
Grade 12 Algebra: Standard Form
A Grade 12 math worksheet focusing on converting between different forms of linear equations, identifying slopes and intercepts, and graphing linear equations in standard form.
Characteristics of Parabolas Worksheet
Explore and identify the key characteristics of parabolas, including vertex, focus, directrix, and axis of symmetry.
Solving Equations with Variables on Both Sides
This worksheet provides practice on solving linear equations where variables appear on both sides of the equals sign.
Evaluating Algebraic Expressions
This worksheet focuses on evaluating complex algebraic expressions involving various operations and functions, suitable for Grade 12 students.
Graphing Parabolas Worksheet
A Grade 12 math worksheet on graphing parabolas, covering standard form, vertex form, and intercepts.
Grade 12 Sigma Notation Worksheet
A comprehensive worksheet for Grade 12 students covering sigma notation, including evaluating sums, expanding series, and writing expressions in sigma notation.