Algebra II - CBA 03

Which equation has exactly 3 real roots?

0 = - x³ + 5x² - 1

Which is equivalent to 7y(y - 2z) - 3y(2y + z)

y² - 17yz

Which expression represents x²( x + 2) - 16(x + 2) factored completely?

(x + 2)(x + 4)(x - 4)

Which expression, when simplified, equals 5x^4 - 2x³ + x

(4x^4 + x³ - x) - (- x^4 + 3x³ - 2x)

What is the quotient when x³ - 4x² + 5x - 2 is divided by x + 2?

x² - 6x +17

What is the quotient when 6x³ + 12x² + 6x + 12 is divided by 3x² + 3?

(2x + 4)

Which of the following is an equivalent expression of (x^4 - 1)?

(x - 1)(x + 1)(x² + 1)

Which expression is equivalent to t³ - 12t² + 36t?

t(t - 6)(t - 6)

What is the factored form of 27p³ - 8q³?

(3p - 2q)(9p² + 6pq + 4q²)

The equation below is true for all values of x, where a and b are constants. What is the value of b/a? (ax + 5)(7x² - bx - 6) = 21x³ + 8x² - 63x - 30

a/b = 1/3

What is the product of (x + y)(4x² - x - 8y² - y)?

4x³ - x² + 4x²y - 2xy - 8xy² - y² - 8y³

What is the next row of Pascal’s Triangle?

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

Expand (a + b)^4.

a^4 + 4a³b + 6a²b² + 4ab³ + b^4

For f(x) = x(x - 4)², choose the answer that correctly describes the graph.

The graph has at least 2 real roots and is not symmetrical with respect to the y-axis or the origin.

Select all true characteristics of the following polynomial: f(x) = x^4 + x³ - 10x² - 4x + 24

• As x → + infinity, y → + infinity

• As x → - infinity, y → + infinity

• The function has at least 3 real roots

• The y-intercept is (0, 24)

• The polynomial has a relative maximum in the interval - 2 < x < 2.

• The graph has exactly 3 turns (changes in direction)

• The graph is not symmetrical

(1, 4, 5, 8, 9, 12, 15)

What is the solution of the equation (x - 12)²/3 = 16?

76

What is the value of x in the equation ³/x + 28 = 4?

36

Which expression is equivalent to ³/27x³/216y^6?

x/2y²

Find the inverse function of f(x) = 1/8x².

f^-1(x) = /8x

Solve for x in the following equation: 4(7x + 18)^1/2 = 4x

x = 9, and x = -2 is extraneous

f(x) = 3/x is transformed to form the new function g(x). To create the new function, it…

g(x) = 2³/2x + 8 - 4

What is the inverse of f(x) = 64x³ - 1?

f^-1(x) = 1/4³/x+1

Which of the following represents the graph of f^-1(x), from question __?

b: horizontal

What is the factored form of f(x) = 64x³ - 1?

(4x - 1)(16x² + 4x + 1)