1.
The excluded value(s) for y^{2} + y + 5 / y + 4 is (are) ___.
Correct Answer
A. Y = -4
Explanation
The excluded value for y in the expression y^2 + y + 5 / y + 4 is y = -4. This is because when y = -4, the denominator of the expression becomes 0, which is undefined. Therefore, y = -4 is excluded from the possible values for y in this expression.
2.
The greatest common factor of x^{5}y and x^{4} y^{2} is ___.
Correct Answer
B. X^{4}y
Explanation
The greatest common factor of x^5y and x^4y^2 is x^4y because it is the highest power of x and y that both terms have in common.
3.
The factorization of 14a + 7b is ___
Correct Answer
C. 7(2a + b)
Explanation
The given expression, 14a + 7b, can be factorized by taking out the common factor of 7. This leaves us with 7(2a + b), which is the correct answer.
4.
Find the trinomial product of (4x + 3) (-2x - 5) : ___.
Correct Answer
C. -8x^{2} - 26x - 15
Explanation
The given trinomial product can be found by multiplying the first terms of both binomials (4x and -2x), then multiplying the outer terms (-5 and 4x), and finally multiplying the last terms (3 and -5). The sum of these three products gives us the trinomial product. In this case, the trinomial product is -8x^2 - 26x - 15.
5.
Find the product of (4a + 3) (4a - 3) : ___.
Correct Answer
C. 16a^{2} - 9
Explanation
The given expression is a product of two binomials. To find the product, we can use the formula for the difference of squares, which states that (a + b)(a - b) = a^2 - b^2. In this case, a = 4a and b = 3. Substituting these values into the formula, we get (4a + 3)(4a - 3) = (4a)^2 - 3^2 = 16a^2 - 9. Therefore, the correct answer is 16a^2 - 9.
6.
The binomial factors of 2x^{2} + 7x + 3 are ___.
Correct Answer
A. (x + 3) (2x + 1)
Explanation
The given expression is a quadratic trinomial. To factorize it, we need to find two binomial factors that when multiplied together, give us the original expression. The correct answer, (x + 3) (2x + 1), is obtained by factoring the trinomial using the distributive property.
7.
Factor 81n^{2} - 100 : ___.
Correct Answer
C. (9n - 10) (9n + 10)
Explanation
The given expression can be factored using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = 9n and b = 10. Therefore, the expression can be factored as (9n - 10)(9n + 10).
8.
The factors of 2 - 98n^{2} are ___.
Correct Answer
A. -2(7n - 1) (7n + 1)
Explanation
The given expression can be factored as -2(7n - 1) (7n + 1). This can be determined by applying the distributive property and factoring out the common factor of -2 from each term.
9.
The factors of 16y^{3} + 68y^{2} + 42y are ___.
Correct Answer
D.
2y(2y + 7) (4y + 3)
Explanation
The given expression can be factored as 2y(2y + 7) (4y + 3). This can be found by looking for common factors and using the distributive property to simplify the expression.
10.
The formula for area is A = lw. If a rectangle has an area of 2x2 + x - 3, its dimensions are ___.
Correct Answer
D.
l: 2x + 3 w: x - 1
Explanation
The correct dimensions of the rectangle are l: 2x + 3 and w: x - 1. This can be determined by substituting these values into the formula for area, A = lw, and simplifying.
11.
A person purchased 5k + 2 items for a total cost of 35k2 + 29k + 6. The average cost per item was ___.
Correct Answer
D. 7k + 3
Explanation
The person purchased 5k + 2 items for a total cost of 35k2 + 29k + 6. To find the average cost per item, we divide the total cost by the number of items. Therefore, the average cost per item is (35k2 + 29k + 6)/(5k + 2). Simplifying this expression, we get 7k + 3.
12.
Correct Answer
D. D
13.
The indicated sum of y/3 + 5y/3 - 4y/3 is _________>
Correct Answer
B. 2y/3
Explanation
The indicated sum of y/3 + 5y/3 - 4y/3 simplifies to (1/3)y + (5/3)y - (4/3)y, which can be further simplified to (6/3)y - (4/3)y. Combining like terms, we get (2/3)y, which is equivalent to 2y/3.
14.
The indicated quotient of ( - 1/3xy) ÷ (-3xy) is ____________.
Correct Answer
D. 1/ 9x^{2}y^{2}
Explanation
The given expression is a quotient of two negative terms, (-1/3xy) and (-3xy). When dividing negative terms, the negative signs cancel out, resulting in a positive quotient. The expression simplifies to 1/3xy divided by 3xy, which can be further simplified to 1/9x^2y^2. Therefore, the correct answer is 1/9x^2y^2.
15.
Correct Answer
D. D