In order to factor the polynomial: $x^3+6x^2+9x$ completely, should you factor out a GCF first? Why or why not?

You encounter the expression: $3x^2+14x+8$. A peer suggests that directly finding integers which will add to 14 and multiply to 8 will factor this expression. Is this suggestion valid? Choose the best justification.

Use the AC method to factor $6x^2+17x+5$.

Factor the polynomial $64m^3-1$.

Use the quadratic formula to solve for: $(x+2)(x+5)-14=0$.

Which statement correctly explains why $(x+3)$ and $(x-3)$ cannot be canceled termwise in a rational expression?

Simplify the multi-step expression to lowest terms: $(\frac{2x}{3y}÷\frac{4x^2}{9y^3})\cdot \frac{27y}{8x}$

Simplify and state excluded values: $\frac{x^2-5x+6}{x^2-4}$

Find the LCD of the denominators $45x$ and $12x^2$.

Simplify: $\frac{x^2-7x+10}{x^2-5x+6}$

Solve $\frac{3}{x+1}-\frac{2}{x^2-1}=\frac{1}{2}$.

According to Boyle's law, gas pressure $p$ varies inversely with volume $V$. If $p=150\text{ kPa}$ when $V=3\text{ L}$, determine the volume when $p=25\text{ kPa}$.

Simplify the expression for any real number $x$: $\sqrt{(x-1{)}^2}$

Simplify $\sqrt{\frac{50x^7}{2x^2}}$.

Simplify $\sqrt[3]{432}$ completely by using prime factorization and extracting perfect cubes.

Rationalize and simplify: $\frac{2+\sqrt{7}}{4-3\sqrt{7}}$

Given $z=-1+2i$, compute the magnitude $\mid z\mid$.