91Ó°ÊÓ

Use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=2 x^{4}+3 x^{3}-11 x^{2}-9 x+15 $$

Write an equation that expresses each relationship. Use \(k\) as the constant of variation. \(s\) is directly proportional to the cube of \(v\)

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$\left(x^{3}-2 x^{2}-5 x+6\right) \div(x-3)$$

In Exercises \(1-8,\) find the domain of each rational function. $$h(x)=\frac{x+7}{x^{2}-49}$$

Consider the equation \(x^{4}+3 x^{3}+2 x^{2}-5 x+12=0\) a. List all possible rational roots. b. Determine whether 1 is a root using synthetic division. What two conclusions can you draw? c. Based on part (b), what possible rational roots can you eliminate? d. Determine whether \(-3\) is a root using synthetic division. What two conclusions can you draw? e. Based on part (d), what possible rational roots can you eliminate?

Write an equation that expresses each relationship. Use \(k\) as the constant of variation. \(r\) varies inversely as \(t\)

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$\left(6 x^{3}+7 x^{2}+12 x-5\right) \div(3 x-1)$$

Use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=4 x^{4}-x^{3}+5 x^{2}-2 x-6 $$

Use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=3 x^{4}-11 x^{3}-3 x^{2}-6 x+8 $$

Divide using long division. State the quotient, \(q(x),\) and the remainder, \(r(x)\). $$\left(6 x^{3}+17 x^{2}+27 x+20\right) \div(3 x+4)$$