Question 1

Simplify the expression $ (x + 1)(x + 5) $. What is the result?

Accepted Answer

$ x^2 + 6x + 5 $

Question 2

Which pair of integers can be used to factor $ x^2 + 7x + 12 $?

Accepted Answer

$ (3, 4) $

Question 3

Factor the trinomial $ n^2 + 9n + 20 $.

Accepted Answer

$ (n + 4)(n + 5) $

Question 4

Which of the following is the correct factorization of $ x^2 - 14x + 49 $? This could represent the area of a square garden with a walkway of width $ x - 7 $ meters.

Accepted Answer

$ (x - 7)^2 $

Question 5

A rectangular field has an area given by $ x^2 + 2x - 8 $. What are the possible dimensions of the field?

Accepted Answer

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

Question 6

Factor $ 4k^2 + 12k + 8 $ completely. This could represent the area of a rectangular patio in square meters.

Accepted Answer

$ 4(k + 1)(k + 2) $

Question 7

Which of the following is the correct factorization for $ y^2 - 6y + 8 $? This could represent the area of a garden where the length is 2 meters more than the width.

Accepted Answer

$ (y - 4)(y - 2) $

Question 8

A company wants to build a rectangular billboard with an area given by $ x^2 - 11x + 28 $. What are the possible dimensions of the billboard?

Accepted Answer

$ (x - 7)(x - 4) $

Question 9

Factor $ 3a^3 + 30a^2 + 63a $ completely. This could represent the total cost (in dollars) of producing $ a $ units of a product, including fixed and variable costs.

Accepted Answer

$ 3a(a + 7)(a + 3) $

Question 10

Which of the following is the correct factorization for $ x^2 + 3x - 70 $? This could represent the profit function for a business.

Accepted Answer

$ (x + 10)(x - 7) $

Question 11

A rectangular garden has an area given by $ m^2 - 8m + 7 $. What are the possible dimensions of the garden?

Accepted Answer

$ (m - 7)(m - 1) $

Question 12

Factor $ 2x^2 - 8x - 24 $ completely. This could represent the area (in square feet) of a rectangular deck.

Accepted Answer

$ 2(x - 6)(x + 2) $

Question 13

Which of the following is the correct factorization for $ k^2 + 13k + 42 $? This could represent the area of a rectangular parking lot.

Accepted Answer

$ (k + 6)(k + 7) $

Question 14

A quadratic equation $ x^2 - 14x - 72 = 0 $ models the profit of a company. What are the possible values of $ x $ where profit is zero?

Accepted Answer

$ x = 18 $ or $ x = -4 $

Question 15

Factor $ 5x^2y - 15xy - 140y $ completely. This could represent the total cost (in dollars) of producing $ x $ units of a product with $ y $ as a variable cost.

Accepted Answer

$ 5y(x - 7)(x + 4) $

Question 16

Which of the following is the correct factorization for $ y^2 + 13y + 40 $? This could represent the area of a rectangular field.

Accepted Answer

$ (y + 5)(y + 8) $

Question 17

A quadratic function $ x^2 - n - 30 $ models the height (in meters) of a projectile. What are the possible values of $ n $ when the height is zero?

Accepted Answer

$ n = 6 $ or $ n = -5 $

Factoring Trinomials and Polynomials: College Algebra Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards