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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