Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Write one example each of a linear, quadratic, and cubic polynomial. Linear: 2x + 3x2+2x

Quadratic: x2+5x+6x3+x+2x

Cubic: x3−2x2+x−1x2+3x+3

(2) Find the degree of the polynomial 5x3−4x^2` + 7.

Correct! The degree is the highest power of x, which is 3.

(3) Write the coefficient of x2 in 4x2 - 3x + 5.

Perfect! The coefficient of x2 is 4.

(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 p(x) is by (x - a), then the remainder is papx−a.

Short Answer Questions (2 Marks Each)

(1) If p(x) = x2 - 3x + 2, find p(2). p(2) =

Perfect! p(2) = 0.

(2) Find the degree and constant term of x4 - 5x3 + 6. Degree: and Constant term:

(3) Using the Remainder Theorem, find the remainder when p(x) = x3 + 2x2 - x + 1 is divided by x - 1. Remainder =

Excellent! Remainder = 3.

(4) If x + 1 is a factor of x3 + kx2 + x + 6, find k. k =

Correct! k = -4.

(5) Write the factor form of x2 + 5x + 6. x+2x+3x−2x+3

Long Answer Questions (4 Marks Each)

(1) Find the remainder when x3 - 6x2 + 11x - 6 is divided by x - 2 using the Remainder Theorem. Remainder =

Perfect! Remainder = 0, so x - 2 is a factor.

(2) Factorize x3 - 3x2 - 4x + 12. x−3x−2x+2x+3x−2x+2

(3) If x - 1 and x - 2 are factors of p(x) = x3 - 3x2 + ax + b, find a and b. a = and b =

(4) Divide x4 - 3x3 + 3x2 - x + 1 by x2 - 2x + 1 and find the quotient and remainder. Quotient: x2−x+1x2−2x+1 and Remainder:

(5) Verify that x - 3 is a factor of x3 - 7x + 6. NoYes

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 2x4 - 5x2 + 3 is:

(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) x3 + 2x2 + 1 (b) x2 + 1 (c) x + 1 (d) x4 + 1

Correct! A cubic polynomial has degree 3.

(3) The remainder when x2 - 4 is divided by x - 2 is:

(a) 0 (b) 4 (c) 2 (d) -4

Correct! By Remainder Theorem: p(2) = 22 - 4 = 0.

(4) The coefficient of x in 3x2 - 4x + 7 is:

(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) x2 - 1 (d) x3 + 2

Correct! A constant polynomial has no variable terms.

(6) If p(x) = x2 - 4x + 3, then p(1) =

(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 x3 - 8 is divided by x - 2 is:

(a) 0 (b) 4 (c) 2 (d) 8

Correct! By Remainder Theorem: p(2) = 23 - 8 = 0.

(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) = x2 - kx + k - 1, then k =

(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