math final

Factor (2x - 1)^3 - 27 as the difference of two cubes. Then, simplify each factor.

(2x - 4)(4x^2 +2x + 7)

Complete the square for the expression x^2 -16x + ___. Write the resulting expression as a binomial squared.

(x - 8)^2

Solve the inequality -8x^2 - 14x + 4 > -11

-2.5 < x < 0.75

for h(x)= 2x^2 + 6x - 9 and k(x)= 3x^2 - 8x + 8, find h(x) - 2k(x)

-4x^2 + 22x - 25

Rewrite the polynomial 12x^2 + 6-7x^5 + 3x^3 + 7x^4 - 5x in standard form. Then, identify the leading coefficient, degree, and number of terms. Name the polynomial

-7x^5 + 7x^4 + 3x^3 + 12x^2 - 5x+6 leading coefficient: -7 degree: 5 number of terms: 6 name: quintic polynomial

Simplify 10 - x^2 - 3x/x^2 + 2x - 8. Identify any x-values for which the expression is undefined.

-x - 5/x + 4; the expression is undefined at x = 2 and x = -4

Use synthetic substitution to evaluate the polynomial P(x) = x^3 -4x^2 + 4x - 5 for x = 4

P(4) = 11

Write the simplest polynomial function with zeroes 5, -4, and 1/2

P(x) = x^3 - 3/2x^2 - 39/2x + 10

Determine whether the data set could represent a quadratic function. Explain. x: -4 -2 0 2 4 y: 15 5 -1 -3 -1

The 2nd differences between y values are constant for equally spaced x-values, so it could represent a quadratic function

Find the number and type of solutions for x^2 - 9x = -8

The equation has two real solutions

Identify the leading coefficient, degree, and end behavior of the function P(x) = -5x^4 - 6x^2 + 6

The leading coefficient is -5, the degree is 4. As x -> -∞, P(x) -> -∞ and as x-> +∞, P(x) -> -∞

Solve the polynomial equation 3x^5 + 6x^4 - 72x^3 = 0 by factoring

The roots are 0, -6, and 4

The volume V of a cylinder varies jointly with the height h and the radius squared r^2, and V = 157.00cm^3 when h = 2cm and r^2 = 25cm. Find V when h= 3cm and r^2 = 36cm^2. Round your answer to the nearest hundredth.

V = 339.12cm^3

What expression is equal to log50?

ln50 divided by ln10

Write the exponential equation 2^3 = 8 in logarithmic form

log(tiny 2)8 = 3

Evaluate log(tiny 4)1/16 by using mental math

log(tiny4)1/16 = -2

Find the absolute value |-7 - 9i|

√130

Find the product (5x - 3)(x^3 - 5x + 2)

5x^4 - 3x^3 - 25x - 6

Simplify 2z^3 - 6z^2/z^2 - 3z. Identify any z-values for which the expression is undefined

2z; z does not equal 3 or 0

Express log(tiny 3)6 + log(tiny 3)4.5 as a single logarithm. Simplify, if possible

3

Simplify the expression log(tiny 4)64

3

Factor the expression 81x^6 + 24x^3 y^3

3x^3 (3x + 2y)(9x^2 - 6xy + 4y^2)

Find the complex conjugate of 3i + 4

4 - 3i

The distance d in meters traveled by a skateboard on a ramp is related to the time traveled in t in seconds. This is modeled by the function: d(t)=4.9t^2 - 2.3t + 5. What is the maximum distance the skateboard can travel, and at what time would it achieve this distance? Round your answers to the nearest hundredth.

4.73 meters at 0.23 seconds

What expression is equivalent to (3-2i)^2

5-12i

Divide by using long divisiom: (5x + 6x^3 - 8)/(x - 2)

6x^2 + 12x + 29 + 50/(x - 2)

Identify the degree of the monomial -5r^3 s^5

8

Write a quadratic function that fits the points (0,6), (2,4), and (3,6)

f(x)= x^2 -3x + 6

Use inverse operations to write the inverse of f(x) = x/4 - 5

f^-1(x) = 4(x + 5)

Let g(x) be a vertical shift of f(x)= -x up 4 units followed by a vertical stretch by a factor of 3. Write the rule for g(x)

g(x) = -3x + 12

Let g(x) be the transformation, vertical translation3 units down, of f(x) = -4x+8. Write the rule for g(x)

g(x) = -4x + 5

The daily profit of a bicycle store can be modeled by f(x) = x^3 - 5x^2 + 2x + 2 where x is the number of bicycles sold. Let g(x) = f(x + 4). Find the rule for g, and explain the meaning of the transformation in terms of daily profit.

g(x) = x^3 + 7x^2 + 10x - 6 The shop makes the same profit after selling 4 fewer bicycles

Solve x^4 - 3x^3 - x^2 - 27x - 90 = 0 by finding all roots

the solutions are 5, -2, 3i, and -3i

Divide by using synthetic division: (x^2 - 9x + 10)/(x - 2)

x - 7 + -4/x - 2

Solve the equation 2x^2 + 18 = 0

x = +-3i

Solve 8^x+8 = 32^x

x = 12

Find the roots of the equation 30x - 45 = x^2 by factoring

x = 3

Solve log(tiny 5)x^10 - log(tiny 5)x^6 = 21

x = 5^21/4

Identify the roots of -3x^3 - 21x^2 + 72x + 540 = 0. State the multiplicity of each root

x-5 is a factor once and x+6 is a factor twice the root 5 has a multiplicity of 1, and the root -6 has a multiplicity of 2

Write an expression that represents the width of a rectangle with length x + 5 and area x^3 + 12x^2 + 47x + 60.

x^2 + 7x + 12