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- Use synthetic division to perform each division. (1/3x^3 - 2/9x^2 + 2/27x - 1/81) / x - 1/3
Problem 17
- Use synthetic division to find ƒ(2). ƒ(x)=x^5+4x^2-2x-4
Problem 18
- Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. ƒ(x)=1/3(x+3)^4-3
Problem 18
- Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. 2x^3+x+2; x+1
Problem 18
- Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. ƒ(x)=1/2(x-2)^2+4
Problem 19
- Use synthetic division to perform each division. (x^4 - 3x^3 - 4x^2 + 12x) / x-2
Problem 19
Problem 19
Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as the second power of x. (y=kx^2)
- Graph the following on the same coordinate system. (a) y = x^2 (b) y = 3x^2 (c) y = 1/3x^2 (d) How does the coefficient of x2 affect the shape of the graph?
Problem 19
Problem 19
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. x2 - 2 > x
- Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1. 2x^4+5x^3-2x^2+5x+6; x+3
Problem 19
Problem 20
Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1.
Problem 21
Write each formula as an English phrase using the word varies or proportional. C=2πr, where C is the circumference of a circle of radius r.
- If ƒ(x) is a polynomial function with real coefficients, and if 7+2i is a zero of the function, then what other complex number must also be a zero?
Problem 21
- Use synthetic division to perform each division. x^3 - 1 / x-1
Problem 21
Problem 21
Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. 2^x2 + 5 ≤ 11x
- Use an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=5x^5+2x^3-3x+4
Problem 21
- Use synthetic division to perform each division. x^4-1 / x-1
Problem 22
- Use an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=-x^3-4x^2+2x-1
Problem 22
- Factor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=2x^3-3x^2-5x+6; k=1
Problem 22
Problem 23
Write each formula as an English phrase using the word varies or proportional. r = d/t, where r is the speed when traveling d miles in t hours.
Problem 23
Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. 23. (a) -x(x - 1)(x - 2) ≥ 0 (b) -x(x - 1)(x - 2) > 0 (c) -x(x - 1)(x - 2) ≤ 0 (d) -x(x - 1)(x - 2) < 0
Problem 23
Use one of the end behavior diagrams below, to describe the end behavior of the graph of each polynomial function.
- Use an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=4x^7-x^5+x^3-1
Problem 24
- Use synthetic division to perform each division. x^7+1 / x+1
Problem 24
Problem 25
Write each formula as an English phrase using the word varies or proportional. V = 1/3 πr^2h, where V is the volume of a cone of radius r and height h
Problem 25
Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (2x - 1)(5x - 9)(x - 4) < 0
- Use an end behavior diagram, , , , or , to describe the end behavior of the graph of each polynomial function. See Example 2. ƒ(x)=9x^6-3x^4+x^2-2
Problem 25
- Factor ƒ(x) into linear factors given that k is a zero. See Example 2. ƒ(x)=-6x^3-25x^2-3x+4; k=-4
Problem 25
- Find a polynomial function ƒ(x) of least degree with real coefficients having zeros as given. √3, -√3, 2, 3
Problem 25
- Use synthetic division to divide ƒ(x) by x-k for the given value of k. Then express ƒ(x) in the form ƒ(x) = (x-k) q(x) + r. ƒ(x) = 2x^3 + 3x^2 - 16x+10; k = -4
Problem 26
