Chapter 5

\(5 x^{2}+3-7 x^{2}-9\)

\(7 y^{2}+5-9 y^{2}-8\)

\(\left(x^{2}-25\right) \div(x+5)\)

\(3 x^{4}+5 y^{2}+8 x^{4}+11 y^{2}\)

\(\left(x^{2}-100\right) \div(x+10)\)

\(8 p^{2}+9 w^{3}+2 p^{2}+13 w^{3}\)

\(\left(8 x^{3}+14 x^{2}+6 x\right) \div(2 x)\)

\(\frac{1}{8} x+\frac{4}{9}-\frac{7}{8} x-\frac{7}{9}\)

\(\left(15 y^{3}+21 y^{2}+54 y\right) \div(3 y)\)

\(\frac{1}{10} a+\frac{5}{12}-\frac{9}{10} a-\frac{1}{12}\)

\(\left(12 a^{4}+6 a^{3}-3 a^{2}\right) \div 3\)

\(\left(18 b^{3}+12 b^{2}-6 b\right) \div 6\)

\(\left(21 a^{3}-7 a\right) \div(7 a)\)

\(\left(24 c^{3}-8 c\right) \div(8 c)\)

\(\left(35 d^{4}-20 d^{3}-5 d^{2}+10 d\right) \div(5 d)\)

A measurement is \(34 \times 10^{12} \mathrm{~km}\). When this measuremen is rewritten in scientific notation, will the exponent be greater or less than 12 ?

\(b^{11} b^{4}\)

\(\left(54 z^{4}-36 z^{3}-6 z^{2}+12 z\right) \div(6 z)\)

\(c^{10} c^{3}\)

\(\left(56 u^{5}-64 u^{3}+72 u^{2}\right) \div\left(8 u^{2}\right)\)

The prefix tri means "three." State an English word besides trinomial that includes the prefix tri. Explain the meaning of the word.

\(\left(9 x^{-3}\right)\left(4 x^{5}\right)\)

\(\left(72 v^{6}-81 v^{4}+54 v^{2}\right) \div\left(9 v^{2}\right)\)

The prefix mono means "one." State an English word besides monomial that includes the prefix mono. Explain the meaning of the word.

A measurement is \(0.000003 \times 10^{4} \mathrm{~g}\). When this measurement is rewritten in scientific notation, will the exponent be greater or less than 4 ?

\(\left(5 y^{7}\right)\left(6 y^{3}\right)\)

\(\left(14 h^{3}-6 h^{2}+12 h\right) \div(-2 h)\)

A student simplified \(3 x+8 x^{2}\) as \(11 x^{3}\). Explain why this is not correct.

\(\frac{x^{9}}{x^{2}}\)

\(\left(20 k^{3}-24 k^{2}+8 k\right) \div(-2 k)\)

\((c+d)(c+d)\)

A student simplified \(3 x+7 y\) as \(10 x y\). Explain why this is not correct.

\(\frac{z^{8}}{z^{3}}\)

\(\left(5 w^{4}-15 w^{2}+60 w+20\right) \div(5 w)\)

\(\frac{32 h^{9}}{8 h^{4}}\)

\(\left(4 p^{4}-16 p^{2}+60 p+20\right) \div(4 p)\)

\(\frac{40 p^{9}}{8 p^{3}}\)

\(\left(5 w^{4}-15 w^{2}+60 w+20\right) \div(-5 w)\)

\(\left(4 \times 10^{3}\right)\left(2 \times 10^{4}\right)\)

\(\left(4 p^{4}-16 p^{2}+60 p+20\right) \div(-4 p)\)

\(\left(3 \times 10^{4}\right)\left(2 \times 10^{5}\right)\)

\(\left(h^{8}-4 h^{2}+100 h+20\right) \div 4\)

\(\left(6 \times 10^{3}\right)\left(2 \times 10^{4}\right)\)

\(-\frac{14 z^{6}}{30 z}\)

\(\left(k^{7}-5 k^{3}+100 k+20\right) \div 5\)

\(\left(8 \times 10^{4}\right)\left(2 \times 10^{5}\right)\)

\(-\frac{18 p^{7}}{40 p}\)

\(\left(h^{8}-4 h^{2}+100 h+20\right) \div\left(4 h^{2}\right)\)

\(\left(6 \times 10^{-3}\right)\left(2 \times 10^{-4}\right)\)

\(\left(u^{2}\right)^{7}\)