2.6.1 Polynomials, factor theorem and algebraic division Quiz: Pearson Edexcel Maths, Unit 2

The 20 questions

1. What is the degree of the polynomial P(x) = 4x^3 - 2x + 7?

   • 7
   • 2
   • 4
   • 3

2. Which term describes a polynomial with the highest power of x equal to two?

   • Quartic
   • Quadratic
   • Linear
   • Cubic

3. What is the remainder when f(x) is divided by (x - a) according to the remainder theorem?

   • f(a)
   • 0
   • f(-a)
   • a

4. If (x - 2) is a factor of f(x), what is the value of f(2)?

   • -2
   • 2
   • 0
   • 1

5. When dividing a cubic polynomial by a linear term, what is the maximum degree of the quotient?

   • 3
   • 4
   • 1
   • 2

6. What type of algebraic fraction is formed by dividing two polynomials?

   • Rational expression
   • Surd expression
   • Exponential term
   • Irrational function

7. In algebraic long division, what operation is used to eliminate the leading term at each step?

   • Subtraction
   • Addition
   • Division
   • Multiplication

8. Which method matches coefficients of corresponding powers of x to find unknown constants?

   • Equating coefficients
   • The factor theorem
   • Polynomial long division
   • Synthetic substitution

9. If f(3) = 0 for a polynomial f(x), which of the following is guaranteed to be a factor?

   • x + 3
   • x - 9
   • x - 3
   • 3x - 1

10. Find the remainder when x^3 - 4x + 1 is divided by (x - 2).

    • 9
    • 0
    • 1
    • -1

11. Determine if (x + 1) is a factor of x^3 + 2x^2 - x - 2.

    • Undefined
    • Cannot tell
    • Yes
    • No

12. What is the remainder when 2x^3 - 5x^2 + x - 3 is divided by (x + 1)?

    • 3
    • -11
    • 11
    • -3

13. If 2x - 1 is a factor of a polynomial f(x), what value must make f(x) equal zero?

    • -1
    • 1
    • 0.5
    • -0.5

14. Divide x^3 + 6x^2 + 11x + 6 by (x + 1). What is the quadratic quotient?

    • x^2 - 5x + 6
    • x^2 + 7x + 6
    • x^2 + 5x + 6
    • x^2 + 5x - 6

15. Find the value of k if (x - 3) is a factor of x^3 - 4x^2 + kx - 3.

    • 10
    • 3
    • 6
    • -10

16. When a polynomial of degree n is divided by a linear term, what is the degree of the remainder?

    • 1
    • n
    • n - 1
    • 0

17. What is the leading coefficient of the polynomial P(x) = 5 - 4x^2 + 7x^4?

    • 7
    • 5
    • 4
    • -4

18. If x^3 + ax^2 - 4x + 12 is divided by (x + 3) and the remainder is zero, find a.

    • -2
    • -4
    • 2
    • 4

19. Which algebraic method is essential for splitting improper rational functions into partial fractions?

    • Completing the square
    • Factor theorem
    • Algebraic division
    • Discriminant test

20. What is the remainder when x^3 + 3x^2 - 2x + 4 is divided by (x - 1)?

    • 8
    • 0
    • 6
    • 4

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