Easy Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write one example each of a linear, quadratic, and cubic polynomial. Linear:
Quadratic:
Cubic:
(2) Find the degree of the polynomial
Correct! The degree is the highest power of x, which is 3.
(3) Write the coefficient of
Perfect! The coefficient of
(4) Find the value of p(x) = 2x + 3 when x = 5.
Excellent! p(5) = 2(5) + 3 = 10 + 3 = 13.
(5) State the Remainder Theorem.
If a
Short Answer Questions (2 Marks Each)
Note: Answer each question with complete working and clear explanations.
(1) If p(x) =
Perfect! p(2) = 0.
(2) Find the degree and constant term of
(3) Using the Remainder Theorem, find the remainder when p(x) =
Excellent! Remainder = 3.
(4) If x + 1 is a factor of
Correct! k = -4.
(5) Write the factor form of
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete working and clear explanations.
(1) Find the remainder when
Perfect! Remainder = 0, so x - 2 is a factor.
(2) Factorize
(3) If x - 1 and x - 2 are factors of p(x) =
(4) Divide
(5) Verify that x - 3 is a factor of
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The degree of the polynomial
(a) 1 (b) 2 (c) 4 (d) 3
Correct! The highest power of x is 4.
(2) Which of these is a cubic polynomial?
(a)
Correct! A cubic polynomial has degree 3.
(3) The remainder when
(a) 0 (b) 4 (c) 2 (d) -4
Correct! By Remainder Theorem: p(2) =
(4) The coefficient of x in
(a) -4 (b) 3 (c) 7 (d) 4
Correct! The coefficient of x is -4.
(5) Which of the following is a constant polynomial?
(a) 7 (b) x + 1 (c)
Correct! A constant polynomial has no variable terms.
(6) If p(x) =
(a) 0 (b) 2 (c) -2 (d) 4
Correct! p(1) = 1 - 4 + 3 = 0.
(7) A polynomial of degree 1 is called:
(a) Linear (b) Quadratic (c) Cubic (d) Constant
Correct! Degree 1 polynomials are linear.
(8) The remainder when
(a) 0 (b) 4 (c) 2 (d) 8
Correct! By Remainder Theorem: p(2) =
(9) The degree of the polynomial 5 is:
(a) 0 (b) 1 (c) 5 (d) Undefined
Correct! A constant polynomial has degree 0.
(10) If x - 1 is a factor of p(x) =
(a) 0 (b) 1 (c) 2 (d) 3
Correct! If x - 1 is a factor, then p(1) = 0: 1 - k + k - 1 = 0, so k = 2.
Basic Polynomial Concepts True or False
Determine whether these statements are True or False:
Polynomials and Factorisation Quiz
🎉 Excellent Work! Polynomial Fundamentals Mastered:
You have successfully completed the "Polynomials and Factorisation (Easy)" worksheet and learned:
(1) Polynomial Classification: Understanding linear, quadratic, cubic, and constant polynomials based on their degrees
(2) Degree Identification: Finding the highest power of the variable to determine polynomial degree
(3) Coefficient Recognition: Identifying coefficients of specific terms in polynomial expressions
(4) Polynomial Evaluation: Substituting values into polynomials to find specific outputs
(5) Remainder Theorem: Understanding that when p(x) is divided by (x - a), the remainder equals p(a)
(6) Factor Theorem: Recognizing that if p(a) = 0, then (x - a) is a factor of p(x)
(7) Basic Factorization: Breaking down simple polynomials into their factor forms
(8) Polynomial Division: Understanding the relationship between divisor, quotient, and remainder
(9) Constant and Variable Terms: Distinguishing between different types of terms in polynomials
(10) Problem-solving with Polynomials: Using polynomial properties to find unknown coefficients
(11) Algebraic Manipulation: Working with polynomial expressions and simplifying them
(12) Mathematical Verification: Checking whether given expressions are factors of polynomials
(13) Polynomial Operations: Basic addition, subtraction, and evaluation of polynomials
(14) Real-world Applications: Understanding how polynomial concepts apply to mathematical modeling
(15) Mathematical Communication: Using correct polynomial terminology and notation
Outstanding foundation! You're ready to explore more advanced polynomial operations and factorization techniques!