Factoring Expressions And Solving Quadratic Equations (Me3e Quiz 1)

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| By Jrivers

Jrivers

Community Contributor

Quizzes Created: 2 | Total Attempts: 470

Questions: 10 | Attempts: 276 | Updated: Mar 21, 2023

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Questions and Answers

1.

Define each term in your own words! a) quadratic equation b) set notation
2.

In order, write down the four steps for solving a quadratic equation.
3.

Factor the following (be careful with signs!)

Correct Answer
(y-7) (y+7)
(y - 7)(y + 7)
(y -7)(y +7)
(y- 7)(y+ 7)

Explanation
This is an example of difference of perfect squares where y2 and 49 are both perfect squares.

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4
4.

Factor the trinomial

Correct Answer
(x + 4) (x - 3)
(x+4)(x-3)
(x+ 4)(x- 3)
(x +4)(x -3)

Explanation
This is a trinomial. We want to multiply to -12 and add to a positive 1. Therefore we need +4 and -3.

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4
5.

TRUE or FALSE The following expression: 3x - 30 is factored correctly as: (x - 10)
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The given expression, 3x - 30, can be factored as 3(x - 10), not as (x - 10). Therefore, the correct answer is False.

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6.

CHECK ALL THAT APPLY Which are factored correctly?
- A.
- B.
- C.
- D.
Correct Answer(s)
A.
C.
7.

Solve the following quadratic equation and choose your answer below
- A.
  
  {-6, -3}
- B.
  
  {-6}
- C.
  
  {3, 6}
- D.
  
  {-3, 6}
Correct Answer
A. {-6, -3}

Explanation
Trinomial factoring

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8.

Solve the following quadratic equation by factoring (HINT: USE GCF)
- A.
  
  {-2/3}
- B.
  
  {-2/3, 0}
- C.
  
  {0}
- D.
  
  {0,3/2}
Correct Answer
A. {-2/3}

Explanation
Factoring by gcf where gcf is just "x"

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9.

Solve and check. Express your answer in set notation { , }

Correct Answer
{-11, 11}
{11, -11}
11, -11
-11, 11

Explanation
The correct answer is {-11, 11},{11, -11}. The answer is in set notation and includes the values -11 and 11, with both possible orders of the numbers. The answer also includes the individual values 11 and -11, but these are not in set notation.

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4
10.

Use the PAYBACK METHOD to factor the following quadratic equation.
- A.
  
  (3x+6)(3x+4)
- B.
  
  (x+2)(x+4)
- C.
  
  (x+6)(x+4)
- D.
  
  (3x+4)(x+2)
Correct Answer
D. (3x+4)(x+2)

Explanation
The given quadratic equation can be factored using the Payback Method. The Payback Method involves finding the common factors between the terms in the equation and factoring them out. In this case, the common factor between the terms is (3x+4). By factoring out (3x+4) from both terms, we are left with (3x+4)(x+2), which is the correct answer.

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