1.
What do A, B, and C represent in the quadratic equation in the AC Method?
Correct Answer
B. The coefficients
Explanation
In the quadratic equation in the AC Method, A, B, and C represent the coefficients. The coefficients are the constants that multiply the variables in the equation. A represents the coefficient of the quadratic term, B represents the coefficient of the linear term, and C represents the constant term. These coefficients determine the shape and position of the quadratic curve. The x-values and y-values, on the other hand, represent the values of the variables and the corresponding output of the equation, respectively.
2.
What is the correct expression to solve for in the AC Method?
Correct Answer
C. Ac + b
Explanation
The correct expression to solve for in the AC Method is ac + b. This method is used to factor quadratic equations of the form ax^2 + bx + c. The AC Method involves finding two numbers, a and c, whose product is equal to ac and whose sum is equal to b. By factoring the quadratic equation using these two numbers, we can find the roots of the equation. Therefore, the correct expression to solve for in the AC Method is ac + b.
3.
What is the first step in the AC method of factoring?
Correct Answer
A. Write in standard form
Explanation
The first step in the AC method of factoring is to write the given equation in standard form. This involves rearranging the terms of the equation so that the highest power of the variable is on the left side and the constant term is on the right side. By doing this, it becomes easier to identify the coefficients of the quadratic equation and proceed with factoring.
4.
The quadratic equation is xÂ² - 7x + 10 = 0. What is the value of AC?
Correct Answer
A. 10
Explanation
In the given quadratic equation xÂ² - 7x + 10 = 0, AC refers to the constant term. The constant term is the term that does not have a variable attached to it. In this equation, the constant term is 10. Therefore, the value of AC is 10.
5.
The quadratic equation is 3x² - 11x - 4 = 0. Which pair adds up to -11 and multiplies to -12?
Correct Answer
D. -8 and 3
Explanation
The quadratic equation is in the form ax² + bx + c = 0. In this case, a = 3, b = -11, and c = -4. We need to find two numbers that add up to -11 and multiply to -12, which are the coefficients of x. The pair that satisfies this condition is -12 and 1. When we substitute these values into the equation, we get 3x² - 12x + 1x - 4 = 0, which simplifies to 3x² - 11x - 4 = 0. Therefore, -12 and 1 are the correct pair.
6.
Using the AC method, what is the factored form of the quadratic equation x² - 8x + 15 = 0?
Correct Answer
A. (x - 5)(x - 3)
Explanation
The factored form of a quadratic equation can be found using the AC method, which involves finding two numbers that multiply to give the product of the coefficient of x² and the constant term (in this case, 1 * 15 = 15) and also add up to give the coefficient of x (in this case, -8). The numbers that satisfy these conditions are -5 and -3. Therefore, the factored form of the quadratic equation x² - 8x + 15 = 0 is (x - 5)(x - 3).
7.
If a = 5, b = 6, and c = 1, which pair of numbers adds up to 6 and multiplies to 5?
Correct Answer
D. -1 and -5
Explanation
The pair of numbers 1 and 5 adds up to 6 (1+ 5 = 6) and multiplies to 5 (1 * 5 = 5).
8.
What is the factored form of the equation 2x² +5x - 3 using the AC method?
Correct Answer
D. (2x - 1)(x + 3)
Explanation
The factored form of the equation 2x² +5x - 3 using the AC method is (2x - 1)(x + 3). This can be found by finding two numbers whose product is equal to the product of the coefficient of the x² term (2) and the constant term (-3), which is -6. The numbers that satisfy this condition are -1 and 6. Then, these numbers are used to split the middle term (-7x) into two terms (-1x and -6x) and factor by grouping. This leads to the factored form of (2x - 1)(x + 3).
9.
For the quadratic equation 3xÂ² - x - 2 = 0, what is the value of AC in the AC method?
Correct Answer
A. -6
Explanation
In the AC method, we need to find two numbers, A and C, such that their product is equal to the product of the coefficient of xÂ² and the constant term (in this case, 3 * -2 = -6). Additionally, these two numbers must add up to the coefficient of x (in this case, -1). By trial and error, we can determine that the numbers -3 and 2 satisfy these conditions (-3 * 2 = -6 and -3 + 2 = -1). Therefore, the value of AC in the AC method for this quadratic equation is -6.
10.
The quadratic equation is 2xÂ² + 5x - 3 = 0. What pair adds up to 5 and multiplies to -6?
Correct Answer
A. -1 and 6
Explanation
The pair -1 and 6 adds up to 5 and multiplies to -6. In the given quadratic equation, the coefficient of x is 5 and the constant term is -3. By factoring the quadratic equation, we need to find two numbers that add up to 5 and multiply to -6. The pair -1 and 6 satisfies these conditions, as -1 + 6 = 5 and -1 * 6 = -6. Therefore, the pair -1 and 6 is the correct answer.
11.
What is the first step in applying the AC method for factoring?
Correct Answer
A. Find two numbers whose product equals the constant term and sum equals the middle coefficient.
Explanation
The first step in the AC method is to find two numbers that satisfy these conditions, as they will help you factor the quadratic expression.
12.
For the expression 4x^2 + 12x + 9, what pair of numbers satisfies the AC Method conditions?
Correct Answer
A. 6 and 6
Explanation
a= 4 b = 12 c = 9. AC = 36. We have to find the factors of 36 where when multiplied we get 36, and when added, we get the b term of 12. Thus, 6+6 = 12 and 6 * 6 = 36.
13.
What is the factored form of the expression 2x^2 + 7x + 3 using the AC Method?
Correct Answer
B. (x + 3)(2x + 1)
Explanation
Applying the AC Method to the given expression, you can factor it as (x + 3)(2x + 1). This factored form is obtained by finding the appropriate pair of numbers and dividing the expression by the leading coefficient.
14.
For the quadratic expression 6x^2 - 13x - 5, what pair of numbers satisfies the AC Method conditions?
Correct Answer
B. 10 and 3
Explanation
To factor the expression 6x^2 - 13x - 5 using the AC Method, you need to find two numbers whose product equals -30 (6 * -5 = -30) and sum equals the middle coefficient (-13). In this case, the pair of numbers is 15 and -2.
15.
What is the factored form of the quadratic expression 5x^2 - 12x - 9 using the AC Method?
Correct Answer
A. (5x + 3)(x - 3)
Explanation
To factor the expression 5x^2 - 12x - 9 using the AC Method, you first find the pair of numbers whose product equals the constant term (-9) and sum equals the middle coefficient (-12). In this case, the pair of numbers is 3 and -3. Afterward, divide the expression by the leading coefficient (5) and rewrite it as (5x + 3)(x - 3).