### Practice Test

For the polynomial $8{y}^{4}-3{y}^{2}+1$

- ⓐ Is it a monomial, binomial, or trinomial?
- ⓑ What is its degree?

In the following exercises, simplify each expression.

$(5{a}^{2}+2a-12)+(9{a}^{2}+8a-4)$

${\left(-\frac{3}{4}\right)}^{3}$

${(10{p}^{3}{q}^{5})}^{2}$

$4u({u}^{2}-9u+1)$

$(m+3)(7m-2)$

$(n-8)({n}^{2}-4n+11)$

$\frac{{5}^{6}}{{5}^{8}}$

${(47{a}^{18}{b}^{23}{c}^{5})}^{0}$

$\frac{8{y}^{2}-16y+20}{4y}$

${4}^{\mathrm{-1}}$

${p}^{\mathrm{-3}}\xb7{p}^{\mathrm{-8}}$

In the following exercises, factor the greatest common factor from each polynomial.

$80{a}^{3}+120{a}^{2}+40a$

According to www.cleanair.org, the amount of trash generated in the US in one year averages out to $\mathrm{112,000}$ pounds of trash per person. Write this number in scientific notation.

Convert $5.25\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-4}}$ to decimal form.

In the following exercises, simplify, and write your answer in decimal form.

$\left(2.4\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{8}\right)\left(2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-5}}\right)$

$\frac{9\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4}}{3\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-1}}}$

A hiker drops a pebble from a bridge $240$ feet above a canyon. The polynomial $\mathrm{-16}{t}^{2}+240$ gives the height of the pebble $t$ seconds a after it was dropped. Find the height when $t=3.$