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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