Question 1

Which of the following is the correct factorization of $$12x^3y^2$ - 8x^2$y^3$$?

Accepted Answer

$$4x^2y^2$(3x - 2y)$

Question 2

A pharmaceutical company needs to design a box with a volume given by $$x^3 - 27$. Which of the following is the complete factorization of this expression?

Accepted Answer

$$(x - 3)(x^2$ + 3x + 9)$$

Question 3

Which of the following is the correct factorization of $$x^2 - 16$?

Accepted Answer

$$(x + 4)(x - 4)$$

Question 4

A rectangular garden has an area represented by $$x^2 + 10x + 25$. What are the possible dimensions of the garden?

Accepted Answer

$$(x + 5)(x + 5)$$

Question 5

Which of the following is the correct factorization of $$2x^2 + 7x + 3$?

Accepted Answer

$$(2x + 1)(x + 3)$$

Question 6

A chemical reaction produces a compound whose mass is modeled by $$8x^3 + 27$. Which of the following is the correct factorization?

Accepted Answer

$$(2x + 3)(4x^2$ - 6x + 9)$$

Question 7

Which of the following is the correct factorization of $$x^2 - 6x + 9$?

Accepted Answer

$$(x - 3)^2$

Question 8

A company wants to create a square tile with an area of $$49y^2 - 25$. What are the possible side lengths of the tile?

Accepted Answer

$$(7y + 5)$$ and $$(7y - 5)$$

Question 9

Which of the following is the correct factorization of $$x^3 + 8$?

Accepted Answer

$$(x + 2)(x^2$ - 2x + 4)$$

Question 10

Which of the following is the greatest common factor (GCF) of $$18x^4y^2$ and 24x^2$y^3$$?

Accepted Answer

$$6x^2y^2$

Question 11

A rectangular field has an area given by $$x^2$$ - $$9y^2. $$Which of the following represents the possible dimensions of the field?

Accepted Answer

$$(x + 3y)(x - 3y)$$

Question 12

Which of the following is the correct factorization of $$x^2 + 12x + 36$?

Accepted Answer

$$(x + 6)^2$

Question 13

Which of the following is the correct factorization of $$x^2 - 2x - 15$?

Accepted Answer

$$(x - 5)(x + 3)$$

Question 14

A company is designing a cylindrical can with a surface area modeled by $$4x^2 - 25$. Which of the following is the correct factorization?

Accepted Answer

$$(2x + 5)(2x - 5)$$

Question 15

Which of the following is the correct factorization of $$x^4 - 16$?

Accepted Answer

$$(x^2 + 4)(x + 2)(x - 2$$)$$

Question 16

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 17

Which of the following is the correct factorization of $$6x^2 - 15x$?

Accepted Answer

$$3x(2x - 5)$$

Question 18

Which of the following is the correct factorization of $$x^2 + 5x + 6$?

Accepted Answer

$$(x + 2)(x + 3)$$

Question 19

Which of the following is the correct factorization of $$x^2 - 4x + 4$?

Accepted Answer

$$(x - 2)^2$

Factoring Polynomials: Fundamental Concepts in College Algebra

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