### Description of Factoring a Polynomial

Factor the following polynomial completely, given that the binomial following it is a factor of the polynomial. x^3 + 2x^2 - 5x - 6, x + 3

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Factor the following polynomial completely, given that the binomial following it is a factor of the polynomial. x^3 + 2x^2 - 5x - 6, x + 3

Factor each difference or sum of cubes. u^3 - 125y^3

Factor the following polynomial completely. -36a^2b + 21ab^2 - 3b^3

1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function and

X>-2y and x-3y<6

X + 8y > 8 and x - 2y < 10

The logarithm transformation can be used A. to overcome violations of the autocorrelation assumption B. to test for possible violations of the autocorrelation assumption C. to change a linear independent variable into a nonlinear independent variable D. to change a nonlinear model into a linear model

1) Using the quadratic equation y = x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by completing the square. c) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is

Using the quadratic equation y = x2 - 6x + 8 = 0, perform the following tasks: a)Solve by factoring, b)solve by completing the square, c)solve by using the quadratic formula

1. Write an equation for the circle that passes through the points: (1, -1), (-5, 7), and (-6, 0). 2. Express the polar equation in rectangular form. 3. Find the total area enclosed by the graph of the polar equation r = 1 + cos 2θ. 4. Write the equation of the line tangent to the parametric curve x = tcos t, y

Assume that (X, d) is a compact metric space, and let f: X -> X be a function such that the inequality d(f(x), f(y)) < d(x, y) holds for all distinct elements x, y in X. Show that f has a unique fixed point. See attached file for full problem description.

1. Graph the inequality. y  1 2. Graph the inequality. y  3x 3. Given f(x) = 4x + 1, find f(3). 4. Given f(x) = 5x2 - 3x + 1, find f(-2). A) -13 B) 15 C) -25 D) 27 5. Given f(x) = x2 + 5x + 3, find f(0). 6. Rewrite the equation 4x - 10y = 11 as a function of x. A) B) C)

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Include the following in your answer: -Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? -Which one of the basic functions (linear, quadratic, ra

Please answer the following questions: 1. Find the domain of the function f(x) = ln(x - 7). 2. Simplify: log 1000 3. Write as a single logarithm (DO NOT find approximations): 2 log 4 + log x - log2. 4. Expand and simplify: ln(e^x). 5. Solve for x: log(x - 4) + log 2 = 1.

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for the su

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign. ADDITIONAL INSTRUCTOR COMMENTS/REQUIREMENTS For unit

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for the

A. what is d, the difference between any 2 terms? answer: show work in this space. b. using the formuls for the nth term of a arithmetic sequence, what is 101st term? answer: show work in this space. c. using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? answer: show work in

2) The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters. a) " in the function's equation. Write h as a function of r. Keep " Answer as interest is c

(See attached file for full problem description) 1. Which of the ordered pairs (3, 1), (0, -4), (-4, 0), (-3, -7) are solutions for the equation x - y = 4? A) (0, -4), (-4, 0), and (-3, -7) B) (-4, 0) and (-3, -7) C) (0, -4) and (-3, -7) D) (3, 1) and (-4, 0) 2. Give the coordinates of the point graphed below.

(See attached file for full problem description with proper symbols) --- 1/ If the amplitude ratio, N in decibels, of an electrical system is given by the formula. N = 10log And the power is given by P = Show that for matched input and output resistances the output voltage Vo is related to the input voltag

For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, A=P [1+r/n}^nt, let r = 10%, P=1, and n= 1 and give the coordinates (t,a) for the points where t= 0,1,2,3,4. Round the A value to the tenth's place. a. show coordinates in this space.

Suppose you deposit $10,000 for 2 years at a rate of 10%. Calculate the return (A) if the bank compounds quarterly (n=4). Round your answer to the hundredth's place. Now calculate the return (A) if the bank compounds monthly (n=12). Now calculate the return (A) if the bank compounds daily (n=365) Show all your work.

An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x donate the length of each side of the square to be cut out. find the function V that represents the volume of the box in terms of x.

(See attached file for full problem description with all symbols) --- Suppose that n is odd and a is a primitive root modulo n. (a) Show that there exists and integer b such that and . (b) Show that b is a primitive root modulo 2n.

Explain an advantage of rational exponents over the radical sign and give an example.

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx +

1) An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Answer b) Graph this fun

While the radical symbol is widely used, converting to rational exponents has advantages. Could you help me understand an advantage of rational exponents over the radical sign. What could be an example of an equation easier to solve as a rational exponent rather then a radical sign.