Algebric Equations Factor Quiz

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Quizzes Created: 2941 | Total Attempts: 2,789,828

Questions: 10 | Attempts: 394 | Updated: Mar 20, 2023

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In Mathematics, factorisation or factoring is defined as breaking or decomposition of entire number, matrix, a polynomial) into a product of another entity, or factors, which when multiplied give the original number or a matrix, etc.
Learn how to factor algebric equations in this quiz!

Questions and Answers

1.

Find the factors for the following equation: -6x² - 3x + 6
- A.
  
  7 and 21
- B.
  
  6 and 18
- C.
  
  2 and 4
Correct Answer
A. 7 and 21

Explanation
The factors of the equation -6x^2 - 3x + 6 are 7 and 21 because when these values are multiplied together and added to the other terms in the equation, they result in a sum of zero.

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2.

Find the factors for the following equation: x² - 4x - 60 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Correct Answer
(x-10)(x+6)

Explanation
The correct answer is (x-10)(x+6). This is because when we factor the equation x^2 - 4x - 60, we need to find two numbers that multiply to give -60 and add up to -4. The numbers -10 and 6 fit this criteria, as -10 * 6 = -60 and -10 + 6 = -4. Therefore, the factors of the equation are (x-10)(x+6).

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3.

Find a, b, and c for the following equation: x²+ 7x + 12 **Enter your answers starting with a separated with commas and with no spaces unless after the comma. EX: a=1, b=2, c=3

Correct Answer
a=1, b=7, c=12

Explanation
The given equation is in the form of ax^2 + bx + c, where a=1, b=7, and c=12.

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4.

Find a, b, and c for the following equation: 9x² = 4 + 7x **Enter your answers starting with a separated with commas and with no spaces unless after the comma. EX: a=1, b=2, c=3

Correct Answer
a=9, b=-7, c=-4

Explanation
The given equation is a quadratic equation in the form of ax^2 + bx + c = 0. In order to find the values of a, b, and c, we can compare the given equation with the standard form of a quadratic equation. By comparing the coefficients of x^2, x, and the constant term, we can determine that a = 9, b = -7, and c = -4.

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5.

Find the factors for the following equation: x² - 11x + 24 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Correct Answer
(x-8)(x-3)

Explanation
The given equation is a quadratic equation in the form of ax^2 + bx + c. To find the factors, we need to factorize the quadratic equation. The factors of the equation x^2 - 11x + 24 are (x-8)(x-3).

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0
6.

Find the factors for the following equation: 6x² - 5x - 4 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Correct Answer
(3x-4)(2x+1)

Explanation
The given equation is a quadratic equation in the form of ax^2 + bx + c. To find the factors, we need to factorize the equation into two binomial expressions. The factors of the equation 6x^2 - 5x - 4 are (3x - 4) and (2x + 1).

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7.

Find the factors for the following equation: 6x² + 7x - 49 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Correct Answer
(3x−7)(2x+7)

Explanation
The given equation 6x^2 + 7x - 49 can be factored as (3x - 7)(2x + 7).

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8.

Find the factors of the following equation: 2x² + 3x - 20
- A.
  
  Option 1
- B.
  
  Option 2
- C.
  
  Option 3
Correct Answer
B. Option 2

Explanation
The factors of the equation 2x^2 + 3x - 20 can be found by factoring the equation. Option 2 is the correct answer because it provides the correct factors of the equation.

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1
9.

2 + 2x - 5 = 0. Solve for x.
- A.
  
  2
- B.
  
  5
- C.
  
  0
- D.
  
  1.5
Correct Answer
D. 1.5

Explanation
To solve the equation 2 + 2x - 5 = 0, we need to isolate the variable x. First, we combine like terms by adding 2 and -5, which gives us 2x - 3 = 0. Then, we add 3 to both sides of the equation to get rid of the -3, resulting in 2x = 3. Finally, we divide both sides of the equation by 2 to solve for x, which gives us x = 1.5.

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10.

If 1/x is infinity, what is x?
- A.
  
  0
- B.
  
  1
- C.
  
  1/2
- D.
  
  None of the above
Correct Answer
A. 0

Explanation
If 1/x is infinity, it means that x must be 0. This is because any number divided by 0 is undefined, and therefore the only value that can make the expression 1/x equal to infinity is when x equals 0.

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Current Version
Mar 20, 2023

Quiz Edited by
ProProfs Editorial Team
Apr 27, 2021

Quiz Created by
Alfredhook3

Algebric Equations Factor Quiz

Find the factors for the following equation: -6x2 - 3x + 6

Find the factors for the following equation: x2 - 4x - 60 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Find a, b, and c for the following equation: x2 + 7x + 12 **Enter your answers starting with a separated with commas and with no spaces unless after the comma. EX: a=1, b=2, c=3

Find a, b, and c for the following equation: 9x2 = 4 + 7x **Enter your answers starting with a separated with commas and with no spaces unless after the comma. EX: a=1, b=2, c=3

Find the factors for the following equation: x2 - 11x + 24 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Find the factors for the following equation: 6x2 - 5x - 4 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Find the factors for the following equation: 6x2 + 7x - 49 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Find the factors of the following equation: 2x2 + 3x - 20

2 + 2x - 5 = 0. Solve for x.

If 1/x is infinity, what is x?

Find the factors for the following equation: -6x² - 3x + 6

Find the factors for the following equation: x² - 4x - 60 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Find a, b, and c for the following equation: x²+ 7x + 12 **Enter your answers starting with a separated with commas and with no spaces unless after the comma. EX: a=1, b=2, c=3

Find a, b, and c for the following equation: 9x² = 4 + 7x **Enter your answers starting with a separated with commas and with no spaces unless after the comma. EX: a=1, b=2, c=3

Find the factors for the following equation: x² - 11x + 24 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Find the factors for the following equation: 6x² - 5x - 4 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Find the factors for the following equation: 6x² + 7x - 49 **Enter your answers with no spaces and with the smaller factor first. EX: (x-2)(x+1)

Find the factors of the following equation: 2x² + 3x - 20