Question 1

Which of the following is the correct factorization of $$3x + 12$$?

Accepted Answer

$$3(x + 4)$$

Question 2

What is the greatest common factor (GCF) of $$12y^2 - 18y$?

Accepted Answer

$$6y$$

Question 3

Factor $$14x^3y^2$ - 28x^2$y^3$$ completely.

Accepted Answer

$$7x^2y^2$(2x - 4y)$

Question 4

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

Accepted Answer

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

Question 5

Given $$x^3 - 27$, which formula should be used to factor it?

Accepted Answer

Difference of cubes: $$a^3$$ - $$b^3 = (a$$ - $$b)(a^2 + ab$$ + $$b^2$$)$$

Question 6

Factor $$x^2 + 7x + 10$ completely.

Accepted Answer

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

Question 7

Which of the following is the correct factorization of $$3x^2 + x - 4$?

Accepted Answer

$$(3x + 4)(x - 1)$$

Question 8

A chemical reaction produces a polynomial $$4x^5$$ - $$36x^3$$ - $$4x^2 + 36$. Factor it completely.

Accepted Answer

$$4(x^2$$ - $$9)(x^3 - 1$$)$$

Question 9

Which of the following is the correct factorization of $$49a^2b$$ + $$10ab^3$$ + $$6ab^2$$?

Accepted Answer

Question 10

A factory produces objects whose area is modeled by $$x^2 - 7x + 10$. What are the possible dimensions?

Accepted Answer

$$(x - 5)$$ and $$(x - 2)$$

Question 11

Which of the following is the correct factorization of $$20x^2$$ - $$45y^2$$?

Accepted Answer

$$5(4x^2$$ - $$9y^2$$)$$

Question 12

Which of the following is the correct factorization of $$27u^3 + 8$?

Accepted Answer

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

Question 13

A medical researcher models the growth of bacteria with $$x^3$$ + $$y^3. $$Which formula should be used to factor this expression?

Accepted Answer

Sum of cubes: $$a^3$$ + $$b^3 = (a$$ + $$b)(a^2 - ab$$ + $$b^2$$)$$

Question 14

Factor $$2x^3$$ - $$10x^2 + 8x$ completely.

Accepted Answer

$$2x(x^2 - 5x + 4$$)$$

Question 15

A company wants to factor $$4m^2 + 3m - 12$ to determine the dimensions of a rectangular plot. What is the correct factorization?

Accepted Answer

$$(4m + 3)(m - 4)$$

Question 16

Which of the following is the correct factorization of $$x^4$$ + $$x^3$$ + $$x^2$$?

Accepted Answer

$$x^2(x^2$ + x + 1)$

Question 17

Which of the following is the correct factorization of $$x^2 - 3x - 4$?

Accepted Answer

$$(x - 4)(x + 1)$$

Question 18

A biologist is studying a population modeled by $$x^3 - 1$. What is the correct factorization?

Accepted Answer

$$(x - 1)(x^2$ + x + 1)$$

Question 19

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Factoring Polynomials in College Algebra: Methods and Applications

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