Polynomials (add, multiply, factor) Knowledge-Based Download PDF

Questions

1. 1.

   Which of the following expressions is equivalent to $(x + y + 2)^2 - (x - y + 2)^2$?

   • A) $2xy + 4y$
   • B) $4xy + 8y$
   • C) $4xy - 8y$
   • D) $4xy + 4y$
2. 2.

   Which of the following is the completely factored form of the polynomial $x^4 - 2x^3 + 2x - 1$ over the integers?

   • A) $(x - 1)(x + 1)^3$
   • B) $(x - 1)^3(x + 1)$
   • C) $(x - 1)^2(x + 1)^2$
   • D) $(x - 1)(x + 1)(x^2 + 1)$
3. 3.

   Which of the following is the completely factored form of the polynomial $x^4 + x^3 + 2x^2 + x + 1$ over the integers?

   • A) $(x^2 + 1)(x^2 + x + 1)$
   • B) $(x^2 - 1)(x^2 + x + 1)$
   • C) $(x^2 + 1)(x^2 - x + 1)$
   • D) $(x^2 + x + 1)^2$
4. 4.

   Which of the following is the completely factored form of the polynomial $x^3 - 6x^2 + 12x - 35$ over the integers?

   • A) $(x - 5)(x^2 + x + 7)$
   • B) $(x + 5)(x^2 - x + 7)$
   • C) $(x - 5)(x^2 - x + 7)$
   • D) $(x - 5)(x^2 - 4x + 7)$
5. 5.

   Which of the following is the expanded form of the polynomial product $(x + 1)(x^2 - x + 1)(x^6 - x^3 + 1)$?

   • A) $x^9 - 1$
   • B) $x^9 + 1$
   • C) $x^{18} + 1$
   • D) $x^9 + x^6 + 1$
6. 6.

   Which of the following is the completely factored form of the polynomial $x^3 - 7x - 6$ over the integers?

   • A) $(x - 1)(x + 2)(x + 3)$
   • B) $(x + 1)(x - 2)(x + 3)$
   • C) $(x + 1)(x + 2)(x - 3)$
   • D) $(x - 1)(x + 2)(x - 3)$
7. 7.

   Which of the following is the completely factored form of the polynomial $x^5 - x^3 - x^2 + 1$ over the integers?

   • A) $(x - 1)(x + 1)^2(x^2 - x + 1)$
   • B) $(x - 1)(x + 1)(x^2 + x + 1)(x^2 - x + 1)$
   • C) $(x - 1)^2(x + 1)(x^2 + x + 1)$
   • D) $(x - 1)^2(x + 1)(x^2 - x + 1)$
8. 8.

   Which of the following is the completely factored form of the polynomial $(x + 1)^3 + (x - 2)^3$ over the integers?

   • A) $(2x - 1)(3x^2 - 3x + 3)$
   • B) $(2x - 1)(x^2 - x + 7)$
   • C) $(2x + 1)(x^2 - x + 7)$
   • D) $(2x - 1)(x^2 + x + 3)$
9. 9.

   Which of the following polynomials is the greatest common factor of $x^3 + x^2 - 4x - 4$ and $x^3 - x^2 - 4x + 4$?

   • A) $x - 2$
   • B) $x + 2$
   • C) $x^2 - 1$
   • D) $x^2 - 4$
10. 10.

    Which of the following is the completely factored form of the polynomial $x^4 + 5x^2 + 9$ over the integers?

    • A) $(x^2 - 3x + 3)(x^2 + 3x + 3)$
    • B) $(x^2 - x + 3)(x^2 + x + 3)$
    • C) $(x^2 - 2x + 3)(x^2 + 2x + 3)$
    • D) $(x^2 - 5x + 9)(x^2 + 5x + 9)$
11. 11.

    Which of the following is the completely factored form of the polynomial $x^6 - 1$ over the integers?

    • A) $(x - 1)(x + 1)(x^4 + x^2 + 1)$
    • B) $(x - 1)(x + 1)(x^2 + x + 1)^2$
    • C) $(x - 1)(x + 1)(x^2 - x + 1)(x^2 + x + 1)$
    • D) $(x - 1)^3(x + 1)^3$
12. 12.

    Which of the following is the completely factored form of the polynomial $4x^2 - 9y^2 - 12x + 9$ over the integers?

    • A) $(2x - 3y + 3)(2x + 3y - 3)$
    • B) $(2x - 3y + 3)(2x + 3y + 3)$
    • C) $(2x - 3y - 3)(2x + 3y - 3)$
    • D) $(2x - 9y - 3)(2x + 9y - 3)$
13. 13.

    Which of the following is the completely factored form of the polynomial $(x^2 - 2x)^2 - 11(x^2 - 2x) + 24$ over the integers?

    • A) $(x + 2)(x + 1)(x - 3)(x - 4)$
    • B) $(x - 2)(x - 1)(x + 3)(x + 4)$
    • C) $(x^2 - 2x - 8)(x^2 - 2x - 3)$
    • D) $(x + 4)(x - 2)(x + 3)(x - 1)$
14. 14.

    If the polynomial equality $(x + 3)(2x^2 + kx - 4) = 2x^3 + 11x^2 + 11x - 12$ is true for all real values of $x$, what is the value of the constant $k$?

    • A) -5
    • B) 8
    • C) 5
    • D) 11
15. 15.

    What is the coefficient of $x^2$ in the expanded form of the polynomial product $(3x^2 - 4x + 2)(2x^2 + 5x - 6)$?

    • A) $-34$
    • B) 34
    • C) $-38$
    • D) $-14$
16. 16.

    Which of the following is the completely factored form of the polynomial $2x^4 - 54x$ over the integers?

    • A) $2x(x - 3)(x^2 + 3x + 9)$
    • B) $2x(x - 3)(x^2 - 3x + 9)$
    • C) $2x(x - 3)^3$
    • D) $2x(x + 3)(x^2 - 3x + 9)$
17. 17.

    Which of the following is the completely factored form of the polynomial $4x^4 - 37x^2 + 9$ over the integers?

    • A) $(4x^2 - 1)(x^2 - 9)$
    • B) $(2x - 3)(2x + 3)(x - 1)(x + 1)$
    • C) $(2x - 1)(2x + 1)(x - 3)(x + 3)$
    • D) $(2x - 1)^2(x - 3)^2$
18. 18.

    Which polynomial is obtained when $3x^3 - 5x^2 + 2x - 8$ is subtracted from the product of $x^2 - 4$ and $3x + 1$?

    • A) $-4x^2 - 10x - 12$
    • B) $6x^3 - 4x^2 - 10x - 12$
    • C) $6x^2 - 14x + 4$
    • D) $6x^2 - 10x - 12$
19. 19.

    Which of the following is the complete factorization of the polynomial $2x^3 - 3x^2 - 8x + 12$ over the integers?

    • A) $(x^2 - 4)(2x - 3)$
    • B) $(x - 2)^2(2x + 3)$
    • C) $(x - 3)(2x - 2)(x + 2)$
    • D) $(x - 2)(x + 2)(2x - 3)$
20. 20.

    Which of the following expressions is equivalent to $(3x - 2)(2x + 5) - 2x(x - 4)$?

    • A) $4x^2 + 3x - 10$
    • B) $4x^2 + 19x - 10$
    • C) $4x^2 + 11x - 10$
    • D) $4x^2 + 19x + 10$