algebra 2a - unit 3: exam

what is the factored form of 121x^4 − 9y^2?

(11x^2 - 3y)(11x^2 + 3y)

which expression correctly shows the factored form of n^3 + 27/125?

(n + 3/5)(n^2 - 3/5n + 9/25)

which polynomial expression is equal to (2 − x)(2 + x)(4 + x^2)?

16 - x^4

which expression correctly shows 2x^3y − 2y factored completely?

2y(x − 1)(x^2 + x + 1)

consider the graph of f(x). https://assets.learnosity.com/organisations/625/asset/media/1236482 which statements are true about the function represented by the graph? select all that apply.

the function is decreasing over (−1.7, 1) the function is increasing over (−∞, −1.7) and (1, ∞) the relative maximum is 9.5, and the relative minimum is 0. as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches infinity, f(x) approaches infinity.

eileen constructed a rectangular metal box that has a width of x inches, a length of 3.5 inches more than its width, and a height 1.75 inches less than its width. considering the graph based on the situation, which statements are true? select all that apply.

the range for the situation involves all y-values greater than 0. the domain for the situation involves all x-values greater than 1.75. to have a volume of approximately 138.13 cubic inches, the width of the box should be 5 inches.

which statements are true about the function f(x) = (x − 2)^2(x + 1)? select all that apply.

the y-intercept is (0, 4) the x-intercepts are (-1, 0) and (2, 0) the domain is all real numbers, and the range is all real numbers.

what are the solutions to the polynomial equation 64x^3 + 1 = 0?

x = -1/4, x = 1 + i√3/ 8, x = 1 - i√3 / 8

if 36, 77, and 85 are the sides of a right triangle, what are the values of x and y?

x = 9 and y = 2

considering the possible values for the volume of the box, which cubic inequality can help eileen find the possible values of the width, x?

x(x + 3.5)(x − 1.75) > 0

eren constructed a rectangular paper box with a volume of 180 in.3. his box has a length of x inches, a width of 5 inches less than its length, and a height 2 inches more than its length. which cubic equation would help eren find the length of the box?

x(x − 5)(x + 2) = 180

for steps 4 through 9, match each numbered statement with the correct reason.

4. distributive property 5. combine like terms 6. substitute 7. commutative property of addition 8. rewrite by using the perfect square trinomial pattern 9. power of a product rule

eren constructed a rectangular paper box with a volume of 180 in.3. his box has a length of x inches, a width of 5 inches less than its length, and a height 2 inches more than its length. what is the length of the box?

7.52 inches

the polynomial function f(a) = a^4 − 81 can be factored as f(a) = (a − 3)(a + 3)(a^2 + 9). what are all of the zeros of the polynomial function?

a = -3, a = 3, a = -3i, and a = 3i

which statement correctly fills in the blank for statement 2 to complete the proof?

a(a^2 - a + 1) + 1(a^2 - a + 1)

#15. which statements are true about the function f(x) = (x − 2)^2(x + 1)? select all that apply.

as x approaches −∞, f(x) approaches −∞, and as x approaches ∞, f(x) approaches ∞. the function has a relative maximum between the x-values −1 and 2, and it has a relative minimum at (2, 0) the function is positive over the intervals (−1, 2) and (2, ∞), and the function is negative over the interval (−∞, −1).

examine the following table, which contains some of the points of a cubic function, f(x). x: -3, -2, -1 f(x): 0, -20, -24 which graph represents the same function?

https://assets.learnosity.com/organisations/625/asset/media/1236705

which graph represents the function that has the rule f(x) = (x − 2)^2(x + 1)?

https://assets.learnosity.com/organisations/625/asset/media/1236949

consider the graph of f(x). https://assets.learnosity.com/organisations/625/asset/media/1236480 which statements are true about the function represented by the graph? select all that apply.

the domain of the function is all real numbers. the range of the function is all real numbers. the x-intercepts are (−3, 0) and (1, 0), and the y-intercept is (0, 3) the function is positive over (−3, 1) and (1, ∞), and negative over (−∞, −3)

examine the following table, which contains some of the points of a cubic function, f(x). x: -3, -2, -1... f(x): 0, -20, -24 which statements can be true about the function represented in the table? select all that apply.

the function has x-intercepts of (−3, 0), (2, 0), and (3, 0), and a y-intercept of (0, -18) as x approaches −∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches −∞. the function has a relative minimum over the interval (0, −2) and a relative maximum over the interval (2,3)