Polynomials (add, multiply, factor) Knowledge-Based Practice

Questions

1. 1.

   Which of the following is the completely factored form of the polynomial $a^3 - a^2b - ab^2 + b^3$?

   • A) $(a + b)^2(a - b)$
   • B) $(a - b)^2(a + b)$
   • C) $(a - b)(a^2 + b^2)$
   • D) $(a - b)^3$
2. 2.

   Which of the following is the completely factored form of the polynomial $(3x - 2)^2 - (x + 4)^2$?

   • A) $4(x - 3)(2x + 1)$
   • B) $(2x - 6)(4x + 2)$
   • C) $4(x + 1)(2x + 1)$
   • D) $2(x - 3)(2x + 1)$
3. 3.

   Which of the following is the completely factored form of the polynomial $12x^2 + 11x - 5$?

   • A) $(3x + 1)(4x - 5)$
   • B) $(6x - 1)(2x + 5)$
   • C) $(4x - 1)(3x + 5)$
   • D) $(3x - 1)(4x + 5)$
4. 4.

   Which of the following polynomials is equivalent to the product $(2x - 1)(x + 2)(x - 3)$?

   • A) $2x^3 + 3x^2 - 11x - 6$
   • B) $2x^3 - x^2 - 13x + 6$
   • C) $2x^3 - 3x^2 - 13x - 6$
   • D) $2x^3 - 3x^2 - 11x + 6$
5. 5.

   Which of the following polynomials is equivalent to the expression $(x + 2)^3 - (x - 2)^3$?

   • A) $12x^2 + 16$
   • B) $12x^2$
   • C) $2x^3 + 24x$
   • D) $12x^2 - 16$
6. 6.

   Which of the following is the completely factored form of the polynomial $x^6 - 64$ over the real numbers?

   • A) $(x - 2)(x + 2)(x^2 - 2x + 4)(x^2 + 2x + 4)$
   • B) $(x - 2)(x + 2)(x^4 + 4x^2 + 16)$
   • C) $(x - 2)^3(x + 2)^3$
   • D) $(x - 2)(x + 2)(x^2 - 4x + 4)(x^2 + 4x + 4)$
7. 7.

   Which of the following is the completely factored form of the polynomial $x^2 - 6x + 9 - 4y^2$?

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

   Which of the following polynomials is equivalent to the expression $(2x^2 - 1)(x^2 + 3) - 2(x^2 - 2)^2$?

   • A) $5x^2 + 5$
   • B) $-3x^2 + 5$
   • C) $13x^2 + 5$
   • D) $13x^2 - 11$
9. 9.

   Which of the following is the completely factored form of the polynomial $x^4 - 13x^2 + 36$?

   • A) $(x^2 - 4)(x^2 - 9)$
   • B) $(x - 2)(x + 2)(x - 3)(x + 3)$
   • C) $(x - 2)^2(x - 3)^2$
   • D) $(x^2 + 4)(x^2 + 9)$
10. 10.

    Which of the following is the completely factored form of the polynomial $8x^3 - 125$ over the real numbers?

    • A) $(2x - 5)(4x^2 - 10x + 25)$
    • B) $(2x - 5)^3$
    • C) $(2x - 5)(4x^2 + 10x + 25)$
    • D) $(2x + 5)(4x^2 - 10x + 25)$
11. 11.

    Which of the following is the completely factored form of the polynomial $2x^3 - 3x^2 - 8x + 12$?

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

    Which of the following polynomials is equivalent to the expression $(3x^2 - 4x + 6) + 2(x^3 - 5x + 1) - (4x^3 + 2x^2 - 7)$?

    • A) $-2x^3 + x^2 - 14x + 15$
    • B) $-2x^3 + x^2 - 14x + 1$
    • C) $-2x^3 + x^2 - 9x + 14$
    • D) $-2x^3 + 5x^2 + 6x + 15$
13. 13.

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

    • A) $2x^3 + 11x^2 - 22x - 15$
    • B) $2x^3 + 5x^2 - 2x + 15$
    • C) $2x^3 + 5x^2 - 22x - 15$
    • D) $2x^3 + 5x^2 - 22x + 15$
14. 14.

    Which of the following is the completely factored form of the polynomial $3x^3 - 3x^2 - 36x$?

    • A) $3x(x + 4)(x - 3)$
    • B) $3x(x - 4)(x + 3)$
    • C) $3x(x - 6)(x + 2)$
    • D) $3(x - 4)(x + 3)$

Answers and step-by-step solutions appear after you finish the test.