Question 1

Which of the following is the Greatest Common Factor (GCF) of the polynomial $4x^2y - 100y$?

Accepted Answer

$4y$

Question 2

Factor the polynomial $x^2 - 13x + 40$ completely.

Accepted Answer

$(x - 5)(x - 8)$

Question 3

A chemical reaction produces a quadratic equation for the concentration of a substance: $x^2 - 2x - 15 = 0$. What are the possible concentrations (solutions) for $x$?

Accepted Answer

$x = 5$ or $x = -3$

Question 4

Which special product formula is used to factor $x^2 - 49$?

Accepted Answer

Difference of Squares: $a^2 - b^2 = (a - b)(a + b)$

Question 5

Factor the polynomial $25x^2 - 110x + 121$ using a special product formula.

Accepted Answer

$(5x - 11)^2$

Question 6

A company’s profit function is $3x^2 - 2x - 5$. To find the break-even points, factor the quadratic. What are the values of $x$?

Accepted Answer

$x = -1$ or $x = \frac{5}{3}$

Question 7

Which of the following is the correct factorization of $x^2 + 12x + 36$?

Accepted Answer

$(x + 6)^2$

Question 8

Factor the polynomial $6x^3 - 2x^2 + 3x - 1$ by grouping.

Accepted Answer

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

Question 9

A biologist models population growth with $4x^2 - 19x + 12$. What is the factored form to find equilibrium points?

Accepted Answer

$(4x - 3)(x - 4)$

Question 10

Which is the correct factorization of $x^2 + 5x + 6$ using the AC method?

Accepted Answer

$(x + 2)(x + 3)$

Question 11

Factor $x^2 - 2x - 15$ using the AC method. What are the factors?

Accepted Answer

$(x - 5)(x + 3)$

Question 12

A physics equation is $x^2 - 5x + 7x + 35$. Factor by grouping.

Accepted Answer

$(x^2 + 7)(x - 5)$

Question 13

Which of the following is the correct factorization of $x^2 - 2x - 15$?

Accepted Answer

$(x - 5)(x + 3)$

Question 14

Factor the polynomial $x^2 - 9$ using a special product formula.

Accepted Answer

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

Question 15

A quadratic model for a medical dosage is $3x^2 - 2x - 5$. What is the factored form?

Accepted Answer

$(3x + 5)(x - 1)$

Question 16

Which is the correct factorization of $x^2 + 7x + 6$?

Accepted Answer

$(x + 1)(x + 6)$

Question 17

Factor $-3x^4 + 12x^3 - 18x^2$ by taking out the GCF.

Accepted Answer

$-3x^2(x^2 - 4x + 6)$

Question 18

A business’s cost function is $x^2 - 2x - 15$. What are the break-even points?

Accepted Answer

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

Question 19

Factor $x^2 + 2x - 35$ using the AC method.

Accepted Answer

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

Factoring Polynomials: Methods and Applications in College Algebra

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