# HomeWorx 02.07.2015

Evan’s algebraic toils continue…

Express as a polynomial
Swok. Cole, P. 43, #11

$$(3x+5)(2x^2+9x-5)$$

Express as a polynomial
Swok. Cole, P. 43, #19

$${\frac{3u^3v^4-2u^5v^2+(u^2v^2)^2}{u^3v^2}}$$

Express as a polynomial
Swok. Cole, P. 44, #35

$$(x^{\frac{1}{3}}-y^{\frac{1}{3}})(x^{\frac{2}{3}}+x^{\frac{1}{3}}y^{\frac{1}{3}}+y^{\frac{2}{3}})$$

Express as a polynomial
Swok. Cole, P. 44, #52

$$121r^3s^4+77r^2s^4-55r^4s^3$$

Simplify
Swok. Cole, P. 54, #27

$${\frac{p^4+3p^3-8p-24}{p^3-2p^2-9p+18}}$$

Simplify
Swok. Cole, P. 55, #71

$$(x^2-4)^{\frac{1}{2}}(3)(2x+1)^2(2)+(2x+1)^3(\frac{1}{2})(x^2-4)^{\frac{-1}{2}} (2x)$$

Simplify
Swok. Cole, P. 55, #81

$${\frac{(4x^2+9)^{\frac{1}{2}}(2)-(2x+3)({\frac{1}{2}})(4x^2x+9)^{\frac{-1}{2}}(8x)}{[(4x^2+9)^{\frac{1}{2}}]^2}}$$

Simplify; rationalize denominator if necessary
Swok. Cole, P. 56, #20

$$\left({\frac{-64x^3}{z^6y^9}}^{\frac{2}{3}}\right)$$

Express in the form a+bi, where a and b are real numbers
Swok. Cole, P. 96, Example 3a
$$4(2+5i)-(3-4i)$$

Express in the form a+bi, where a and b are real numbers
Swok. Cole, P. 96, Example 3c

$$i(3-2i)^2$$

Express in the form a+bi, where a and b are real numbers
Swok. Cole, P. 98, Example 4a

$${\frac{1}{9+2i}}$$

Express in the form a+bi, where a and b are real numbers
Swok. Cole, P. 98, Example 4b

$${\frac{7-i}{3-5i}}$$

Express in the form a+bi, where a and b are real numbers
Swok. Cole, P. 99, Example 5

$$(5-\sqrt-9)(-1+\sqrt-4)$$

Solve the equation (and make your steps as long and difficult as possible)
Swok. Cole, P. 108, #11

$$y^{\frac{3}{2}}=5y$$

Solve the equation (make your work count, but don’t count on it working)
Swok. Cole, P. 108, #31

$$\large\sqrt{2\sqrt{3x+1}} = \sqrt{3x-5}$$

Solve the equation (show your work, though I bet it will SHOW YOU first)
Swok. Cole, P. 108, #33

$$\large\sqrt{1 +4\sqrt x}=\large \sqrt x+1$$

Solve the equation (just f_ck_n’ solve it, man)
Swok. Cole, P. 108, #35

$$x^4-25x^2+144=0$$

Solve the equation (and destroy it in the process)
Swok. Cole, P. 108, #45

$$\left(\frac {t}{t+1}\right)^2-\frac{2t}{t+1}-8=0$$

Solve for the specified variable
Swok. Cole, P. 108, #53

$$\text{Period of a pendulum:}$$

$$T=2\pi\sqrt\frac{l}{2}\text{ for }l$$

Solve for inequality; express solutions in terms of intervals when able
Swok. Cole, P. 118, #35

$$0\leq4-\frac{1}{3}x<2$$

Solve for inequality; express solutions in terms of intervals when able
Swok. Cole, P. 118, #63

$$\left| \frac{2-3x}{5} \right|\geq2$$

Solve the equation
Swok. Cole, P. 127, #5

$$\frac{1}{\sqrt x}-2=\frac{1-2\sqrt x}{\sqrt x}$$

Solve the equation by completing the square
Swok. Cole, P. 127, #29

$$-\frac{1}{2}<\frac{2x+3}{5}<\frac{3}{2}$$

Solve for the specified variable
Swok. Cole, P. 127, #48

$$\text{Volume of a frustum cone:}$$

$$V=\frac{1}{3}\pi h(r^2 +R^2+rR)\text{ for }r$$

(We may need a separate sheet of paper.)