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For the following problems, write the number of terms that appear, then write the terms.
$4{x}^{2}+7x+12$
$\text{three:\hspace{0.17em}}4{x}^{2},7x,12$
$14{y}^{6}$
List, if any should appear, the common factors for the following problems.
$9{y}^{4}-18{y}^{4}$
$6(a+4)+12(a+4)$
$17{x}^{2}y(z+4)+51y(z+4)$
For the following problems, answer the question of how many.
$x\text{'}\text{s}\text{\hspace{0.17em}}\text{in}\text{\hspace{0.17em}}9x?$
$(a+b)\text{'}\text{s}\text{\hspace{0.17em}}\text{in}\text{\hspace{0.17em}}\text{12}(a+b)?$
12
${a}^{4}\text{'}\text{s}\text{\hspace{0.17em}}\text{in}\text{\hspace{0.17em}}6{a}^{4}?$
${c}^{3}\text{'}\text{s}\text{\hspace{0.17em}}\text{in}\text{\hspace{0.17em}}2{a}^{2}b{c}^{3}?$
$2{a}^{2}b$
${(2x+3y)}^{2}\text{'}\text{s}\text{\hspace{0.17em}}\text{in}\text{\hspace{0.17em}}5(x+2y){(2x+3y)}^{3}?$
For the following problems, a term will be given followed by a group of its factors. List the coefficient of the given group of factors.
$16{a}^{3}{b}^{2}{c}^{4},\text{\hspace{0.17em}}{c}^{4}$
$(-5){a}^{5}{b}^{5}{c}^{5},\text{\hspace{0.17em}}bc$
For the following problems, observe the equations and write the relationship being expressed.
$a=3b$
$\text{The\hspace{0.17em}value\hspace{0.17em}of\hspace{0.17em}}a\text{\hspace{0.17em}is\hspace{0.17em}equal\hspace{0.17em}to\hspace{0.17em}three\hspace{0.17em}time\hspace{0.17em}the\hspace{0.17em}value\hspace{0.17em}of\hspace{0.17em}}b\text{.}$
$r=4t+11$
$f=\frac{1}{2}{m}^{2}+6g$
$\text{The\hspace{0.17em}value\hspace{0.17em}of\hspace{0.17em}}f\text{\hspace{0.17em}is\hspace{0.17em}equal\hspace{0.17em}to\hspace{0.17em}six\hspace{0.17em}times\hspace{0.17em}}g\text{\hspace{0.17em}more\hspace{0.17em}then\hspace{0.17em}one\hspace{0.17em}half\hspace{0.17em}time\hspace{0.17em}the\hspace{0.17em}value\hspace{0.17em}of\hspace{0.17em}}m\text{\hspace{0.17em}squared}\text{.}$
$x=5{y}^{3}+2y+6$
${P}^{2}=k{a}^{3}$
$\text{The\hspace{0.17em}value\hspace{0.17em}of\hspace{0.17em}}P\text{\hspace{0.17em}squared\hspace{0.17em}is\hspace{0.17em}equal\hspace{0.17em}to\hspace{0.17em}the\hspace{0.17em}value\hspace{0.17em}of\hspace{0.17em}}a\text{\hspace{0.17em}cubed\hspace{0.17em}times\hspace{0.17em}}k\text{.}$
Use numerical evaluation to evaluate the equations for the following problems.
$\begin{array}{ll}C=2\pi r.\hfill & \text{Find}\text{\hspace{0.17em}}C\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}\pi \text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{approximated}\text{\hspace{0.17em}}\text{by}\text{\hspace{0.17em}}\hfill \\ \hfill & 3.14\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}r=6.\hfill \end{array}$
$\begin{array}{cc}I=\frac{E}{R}.& \text{Find}\text{\hspace{0.17em}}I\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}E=20\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}R=2.\end{array}$
10
$\begin{array}{cc}I=prt.& \text{Find}\text{\hspace{0.17em}}I\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}p=1000,\text{\hspace{0.17em}}r=0.06,\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}t=3.\end{array}$
$\begin{array}{cc}E=m{c}^{2}.& \text{Find}\text{\hspace{0.17em}}E\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}m=120\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}c=186,000.\end{array}$
$\text{4}\text{.1515}\times {\text{10}}^{12}$
$\begin{array}{ll}z=\frac{x-u}{s}.\hfill & \text{Find}\text{\hspace{0.17em}}z\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}x=42,\text{\hspace{0.17em}}u=30,\text{\hspace{0.17em}}\text{and}\hfill \\ s=12.\hfill & \hfill \end{array}$
$\begin{array}{ll}R=\frac{24C}{P(n+1)}.\hfill & \text{Find}\text{\hspace{0.17em}}R\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}C=35,\text{\hspace{0.17em}}P=300,\text{\hspace{0.17em}}\text{and}\hfill \\ n=19.\hfill & \hfill \end{array}$
$\frac{7}{50}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}0.14$
For the following problems, classify each of the polynomials as a monomial, binomial, or trinomial. State the degree of each polynomial and write the numerical coefficient of each term.
$10{a}^{4}$
$4xy+2y{z}^{2}+6x$
$9a{b}^{2}{c}^{2}+10{a}^{3}{b}^{2}{c}^{5}$
binomial; tenth; 9, 10
$\begin{array}{cc}{(2x{y}^{3})}^{0},& x{y}^{3}\ne 0\end{array}$
Why is the expression $\frac{4x}{3x-7}$ not a polynomial?
. . . because there is a variable in the denominator
Why is the expression $5{a}^{3/4}$ not a polynomial?
For the following problems, classify each of the equations by degree. If the term linear, quadratic, or cubic applies, use it.
$4{a}^{2}-5a+8=0$
$5{x}^{2}+2{x}^{2}-3x+1=19$
Simplify the algebraic expressions for the following problems.
$4{a}^{2}b+8{a}^{2}b-{a}^{2}b$
$21{x}^{2}{y}^{3}+3xy+{x}^{2}{y}^{3}+6$
$22{x}^{2}{y}^{3}+3xy+6$
$7(x+1)+2x-6$
$5[3x+7(2{x}^{2}+3x+2)+5]-10{x}^{2}+4(3{x}^{2}+x)$
$8\{3[4{y}^{3}+y+2]+6({y}^{3}+2{y}^{2})\}-24{y}^{3}-10{y}^{2}-3$
$120{y}^{3}+86{y}^{2}+24y+45$
$4{a}^{2}b{c}^{3}+5ab{c}^{3}+9ab{c}^{3}+7{a}^{2}b{c}^{2}$
$4k(3{k}^{2}+2k+6)+k(5{k}^{2}+k)+16$
$9{x}^{2}y(3xy+4x)-7{x}^{3}{y}^{2}-30{x}^{3}y+5y({x}^{3}y+2x)$
$3m[5+2m(m+6{m}^{2})]+m({m}^{2}+4m+1)$
$36{m}^{4}+7{m}^{3}+4{m}^{2}+16m$
$2r[4(r+5)-2r-10]+6r(r+2)$
$abc(3abc+c+b)+6a(2bc+b{c}^{2})$
$3{a}^{2}{b}^{2}{c}^{2}+7ab{c}^{2}+a{b}^{2}c+12abc$
${s}^{10}(2{s}^{5}+3{s}^{4}+4{s}^{3}+5{s}^{2}+2s+2)-{s}^{15}+2{s}^{14}+3s({s}^{12}+4{s}^{11})-{s}^{10}$
$2{x}^{2}{y}^{4}(3{x}^{2}y+4xy+3y)$
$5{m}^{6}(2{m}^{7}+3{m}^{4}+{m}^{2}+m+1)$
$10{m}^{13}+15{m}^{10}+5{m}^{8}+5{m}^{7}+5{m}^{6}$
${a}^{3}{b}^{3}{c}^{4}(4a+2b+3c+ab+ac+b{c}^{2})$
$(y+4)(y+5)$
$(3x+4)(2x+6)$
$5a{b}^{2}-3(2a{b}^{2}+4)$
$5{x}^{2}+2x-3-7{x}^{2}-3x-4-2{x}^{2}-11$
$7x({x}^{2}-x+3)$
$4{x}^{2}{y}^{2}(2x-3y-5)-16{x}^{3}{y}^{2}-3{x}^{2}{y}^{3}$
$-5y({y}^{2}-3y-6)-2y(3{y}^{2}+7)+(-2)(-5)$
$-11{y}^{3}+15{y}^{2}+16y+10$
$-[-(-4)]$
${x}^{2}+3x-4-4{x}^{2}-5x-9+2{x}^{2}-6$
$4{a}^{2}b-3{b}^{2}-5{b}^{2}-8{q}^{2}b-10{a}^{2}b-{b}^{2}$
$-6{a}^{2}b-8{q}^{2}b-9{b}^{2}$
$2{x}^{2}-x-(3{x}^{2}-4x-5)$
$-6(a+2)-7(a-4)+6(a-1)$
Add $4({x}^{2}-2x-3)$ to $-6({x}^{2}-5)$ .
$(x+4)(x-6)$
$(2a-5)(5a-1)$
${(a-3)}^{2}$
${(x-y)}^{2}$
${(3a-5b)}^{2}$
$(k+6)(k-6)$
$(a-2)(a+2)$
$(4a+3b)(4a-3b)$
$(2y+5)(4y+5)$
$(6+a)(6-3a)$
$6(a-3)(a+8)$
$x(x-7)(x+4)$
${m}^{2}n(m+n)(m+2n)$
${m}^{4}n+3{m}^{3}{n}^{2}+2{m}^{2}{n}^{3}$
$(b+2)({b}^{2}-2b+3)$
$3p({p}^{2}+5p+4)({p}^{2}+2p+7)$
$3{p}^{5}+21{p}^{4}+63{p}^{3}+129{p}^{2}+84p$
${(a+6)}^{2}$
${(2x-3)}^{2}$
${(2m-5n)}^{2}$
${(3{x}^{2}{y}^{3}-4{x}^{4}y)}^{2}$
$9{x}^{4}{y}^{6}-24{x}^{6}{y}^{4}+16{x}^{8}{y}^{2}$
${(a-2)}^{4}$
Find the domain of the equations for the following problems.
$y=5{x}^{2}-2x+6$
$m=\frac{-2x}{h}$
$z=\frac{4x+5}{y+10}$
$x\text{\hspace{0.17em}can\hspace{0.17em}equal\hspace{0.17em}any\hspace{0.17em}real\hspace{0.17em}number;\hspace{0.17em}}y\text{\hspace{0.17em}can\hspace{0.17em}equal\hspace{0.17em}any\hspace{0.17em}number\hspace{0.17em}except}-10$
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