Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Find the degree of the polynomial
Perfect! The degree is the highest power of the variable, which is 4.
(2) Is
Correct! A polynomial cannot have fractional or negative powers.
(3) Write the coefficient of x in
Excellent! The coefficient is the number multiplying the variable.
(4) Write a polynomial in one variable with 3 terms.
Great! A trinomial has exactly three terms.
(5) How many terms are there in
Correct! Count each separate part:
(6) If p(x) =
Perfect! Substitute x = 0: p(0) = 0² - 2(0) + 1 = 1.
(7) What is the remainder when
Excellent! Using remainder theorem: p(2) = 4 - 10 + 6 = 0.
(8) Write a cubic polynomial.
Great! A cubic polynomial has degree 3.
(9) What is the degree of the zero polynomial?
Correct! The zero polynomial (p(x) = 0) has no degree defined.
(10) State True or False: "Every constant is a polynomial."
Perfect! Constants like 5, -2, 0 are polynomials of degree 0 (except 0).
Short Answer Questions (2 Marks Each)
Answer each question in 2-3 sentences
(1) Add the polynomials:
Excellent! Add coefficients of like terms:
(2) Subtract:
Perfect! Change signs and add:
(3) If p(x) =
Correct! p(-1) = 3(1) + 5 + 2 = 10.
(4) Identify the degree and number of terms of p(x) =
Degree:
Number of terms:
Great! Highest power is 5, and there are 4 separate terms.
(5) Verify whether x = 1 is a zero of the polynomial p(x) =
Perfect! Since p(1) = 0, x = 1 is indeed a zero.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Multiply:
(a)
(b)
Excellent work! Remember to distribute each term carefully.
(2) Factorise:
(a)
(b)
Great! Recognizing perfect squares makes factoring easier.
(3) Divide
Quotient:
Remainder:
Perfect! Since remainder is 0, (x + 1) is a factor of the polynomial.
(4) If x = 2 and x = -3 are zeros of p(x) =
Value of a:
Value of b:
Excellent! Using the relationship between zeros and coefficients.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The degree of
(a) 3 (b) 5 (c) 2 (d) 7
Correct! The highest power of x is 5, so the degree is 5.
(2) Which one is not a zero of
(a) 2 (b) 3 (c) 1 (d) None of these
Correct! The zeros are 2 and 3. When x = 1: 1 - 5 + 6 = 2 ≠ 0.
(3) The remainder when
(a) 0 (b) 2 (c) 3 (d) 4
Correct! Using remainder theorem: p(-1) = 1 - 4 + 3 = 0.
(4) The value of x for which p(x) = 0 is called:
(a) root (b) degree (c) term (d) exponent
Correct! A root (or zero) is a value that makes the polynomial equal to zero.
(5) Which of the following is a quadratic polynomial?
(a)
Correct! A quadratic polynomial has degree 2.
(6) If p(x) =
(a) 0 (b) 2 (c) -1 (d) 1
Correct! p(3) = 9 - 12 + 3 = 0.
(7) Number of terms in
(a) 2 (b) 3 (c) 1 (d) 4
Correct! Three terms:
(8) A polynomial of degree 3 is called:
(a) Linear (b) Quadratic (c) Cubic (d) None
Correct! Degree 1 = Linear, Degree 2 = Quadratic, Degree 3 = Cubic.
(9) Which of the following can be factored as (x + 3)(x + 2)?
(a)
Correct! (x + 3)(x + 2) =
(10) A polynomial of the form ax + b is:
(a) Linear (b) Quadratic (c) Constant (d) Trinomial
Correct! A polynomial of degree 1 is called linear.
Polynomial Statements Challenge
Determine whether these statements about polynomials are True or False: