Question 1

Which of the following is the correct factorization of $x^3 + 64$?

Accepted Answer

$ (x + 4)(x^2 - 4x + 16) $

Question 2

A pharmaceutical company needs to package a chemical whose formula is $x^2 - 25$. Which method should they use to factor this expression for calculating the amount of packaging material needed?

Accepted Answer

Difference of two squares

Question 3

Which of the following polynomials is prime over the real numbers?

Accepted Answer

$ x^2 + 8 $

Question 4

A medical researcher models the growth of bacteria with $x^2 + 8x + 16$. What is the correct factorization to predict the population after 4 hours?

Accepted Answer

$ (x + 4)^2 $

Question 5

Which of the following is the correct factorization of $x^4 - 625$?

Accepted Answer

$ (x - 5)(x + 5)(x^2 + 25) $

Question 6

A company wants to maximize profit modeled by $3x^2 - x - 4$. What is the correct factorization to help them find the break-even points?

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

A chemical reaction is modeled by $x^2 + 2x - 15$. What are the roots of the equation after factoring?

Accepted Answer

$ x = -3 $ and $ x = 5 $

Question 9

Which of the following is the correct factorization of $3x^2 + 10x + 3$?

Accepted Answer

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

Question 10

A biologist is analyzing the polynomial $x^3 - 27$ to model cell division. What is the correct factorization?

Accepted Answer

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

Question 11

Which of the following is the correct factorization of $4x^2 + 12x + 9$?

Accepted Answer

$ (2x + 3)^2 $

Question 12

A historian models population growth with $9x^2 + 24x + 16$. What is the correct factorization?

Accepted Answer

$ (3x + 4)^2 $

Question 13

Which of the following is the correct factorization of $x^2 + 9x + 14$?

Accepted Answer

$ (x + 2)(x + 7) $

Question 14

Which of the following is the correct factorization of $x^2 - 7x + 10$?

Accepted Answer

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

Question 15

A company wants to factor $5x^3 - 4x^2$ to analyze production rates. What is the correct factorization?

Accepted Answer

$ x^2(5x - 4) $

Question 16

Which of the following is the correct factorization of $8x^2 + 12x$?

Accepted Answer

$ 4x(2x + 3) $

Question 17

A scientist needs to complete the square for $x^2 + 10x$. What number must be added to complete the square, and what is the resulting expression?

Accepted Answer

Add $25$; result: $x^2 + 10x + 25 = (x + 5)^2$

Question 18

Which of the following is the correct factorization by grouping for $3x^2 - 3x + 2x - 2$?

Accepted Answer

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

Question 19

A factory models its output with $5(x - 2)^3(x + 1)^3 + 4(x - 2)^4(x + 1)^2$. What is the correct factorization by grouping?

Accepted Answer

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

Factoring Polynomials: Methods and Applications

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