Question 1

Which of the following is the correct standard form of a quadratic equation?

Accepted Answer

$ax^2 + bx + c = 0$

Question 2

Given the equation $-4x^2 + x = 8$, what are the values of $a$, $b$, and $c$ when written in standard form?

Accepted Answer

$a = -4$, $b = 1$, $c = -8$

Question 3

What is the first step when factoring any polynomial according to the flowchart?

Accepted Answer

Factor out the greatest common factor (GCF)

Question 4

Which factoring formula matches the expression $(a+b)^2$?

Accepted Answer

$(a+b)^2 = a^2 + 2ab + b^2$

Question 5

If you are given $x^2 - 9x = -20$, what is the equation in standard form?

Accepted Answer

$x^2 - 9x + 20 = 0$

Question 6

How many solutions does a quadratic equation typically have?

Accepted Answer

2

Question 7

Which of the following is a correct factorization of $x^2 - 6x = 0$?

Accepted Answer

$x(x - 6) = 0$

Question 8

What are the solutions to the equation $x^2 - 9x + 20 = 0$?

Accepted Answer

$x = 4$ and $x = 5$

Question 9

Which method should be used to factor a polynomial with four terms?

Accepted Answer

Grouping

Question 10

Given $2x^2 + 7x + 6 = 0$, which pair of numbers multiplies to $12$ and adds to $7$?

Accepted Answer

$3$ and $4$

Question 11

What is the factored form of $x^2 + 3x - 4 = 0$?

Accepted Answer

$(x + 4)(x - 1) = 0$

Question 12

If $x^2 - 5x + 4 = 0$, what are the solutions for $x$?

Accepted Answer

$x = 1$ and $x = 4$

Question 13

Which of the following is NOT a correct step in solving a quadratic equation by factoring?

Accepted Answer

Divide both sides by $x$

Question 14

A chemical reaction produces a quadratic equation for the concentration of a substance: $c^2 - 2c - 8 = 0$. What are the possible concentrations?

Accepted Answer

$c = 4$ and $c = -2$

Question 15

Which formula is used for the difference of squares?

Accepted Answer

$(a + b)(a - b) = a^2 - b^2$

Question 16

A medical dosage calculation leads to the equation $d^2 + 5d + 6 = 0$. What are the possible dosages?

Accepted Answer

$d = -2$ and $d = -3$

Question 17

Which step comes immediately after factoring completely when solving a quadratic equation by factoring?

Accepted Answer

Set each factor equal to zero

Question 18

If a quadratic equation has only one term, which factoring method should you use according to the flowchart?

Accepted Answer

Factor out the GCF

Question 19

A quadratic equation $x^2 + bx + c = 0$ has roots $x = 2$ and $x = 5$. What are the values of $b$ and $c$?

Accepted Answer

$b = -7$, $c = 10$

Question 20

Which of the following is the correct factorization for $2x^2 + 7x + 6 = 0$?

Accepted Answer

$(2x + 3)(x + 2) = 0$

Factoring and Solving Quadratic Equations: College Algebra Study Notes

Study Guide - Practice Questions