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 $$ 5x^2$y - 15xy - 140y $$ 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

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