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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:
-6x^{2} - 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:
x^{2} - 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:
x^{2 }+ 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:
9x^{2} = 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:
x^{2} - 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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6.
Find the factors for the following equation:
6x^{2} - 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:
6x^{2} + 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:
2x^{2} + 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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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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