Algebric Equations Factor Quiz

1. 2 + 2x - 5 = 0. Solve for x.

2

5

0

1.5

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.

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.

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

7 and 21

6 and 18

2 and 4

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.

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.

3. If 1/x is infinity, what is x?

0

1

1/2

None of the above

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.

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.

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

Option 1

Option 2

Option 3

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.

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.

5. 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)

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).

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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6. 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

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

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).

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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8. 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

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.

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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9. 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)

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).

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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