91Ó°ÊÓ

a. List all possible rational zeros. b. Use synthetic division to test the possible rational zeros and find an actual zero. c. Use the quotient from part ( \(b\) ) to find the remaining zeros of the polynomial function. $$f(x)=x^{3}-2 x^{2}-11 x+12$$

Solve each polynomial inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2}-2 x+1>0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies jointly as \(m\) and the square of \(n\) and inversely as \(p\) \(y=15\) when \(m=2, n=1,\) and \(p=6 .\) Find \(y\) when \(m=3, n=4,\) and \(p=10\).

Divide using long division. State the quotient, q(x), and the remainder, r(x). $$\frac{3 x^{2}-2 x+5}{x-3}$$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=-3(x-2)^{2}+12$$

a. List all possible rational zeros. b. Use synthetic division to test the possible rational zeros and find an actual zero. c. Use the quotient from part ( \(b\) ) to find the remaining zeros of the polynomial function. $$f(x)=2 x^{3}-3 x^{2}-11 x+6$$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. $$f(x)=-2(x+1)^{2}+5$$

Solve each polynomial inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$ 3 x^{2}+10 x-8 \leq 0 $$

Divide using long division. State the quotient, q(x), and the remainder, r(x). $$\frac{4 x^{4}-4 x^{2}+6 x}{x-4}$$

Solve each polynomial inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$ 9 x^{2}+3 x-2 \geq 0 $$