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

스터디 가이드 - 연습 문제