Chapter 1

Factor out the greatest common factor. $$ 6 x^{4} y-4 x^{2} y^{2}+2 x^{2} y^{3} $$

Classify the number as to type. (For example, \(\frac{1}{2}\) is rational and real, whereas \(\sqrt{5}\) is irrational and real.) $$ -\sqrt{5} $$

Evaluate the expression. $$ -\left(-\frac{4}{5}\right)^{3} $$

Solve the equation by factoring, if required: $$ 4 t^{2}+2 t-2=0 $$

Show the interval on a number line. $$ [-1,4) $$

simplify the expression. \(\frac{x^{2}+x-2}{x^{2}+3 x+2}\)

Rewrite the number without radicals or exponents.. $$ 8^{2 / 3} $$

Solve the given equation. $$ -2 y+3=-7 $$

Rewrite the number without using exponents. $$ 2^{-2}+3^{-1} $$

Factor out the greatest common factor. $$ 3 x(2 x+1)-5(2 x+1) $$

Classify the number as to type. (For example, \(\frac{1}{2}\) is rational and real, whereas \(\sqrt{5}\) is irrational and real.) $$ \frac{\pi}{2} $$

Evaluate the expression. $$ -2\left(\frac{3}{5}\right)^{3} $$

Solve the equation by factoring, if required: $$ -6 x^{2}+x+12=0 $$

Show the interval on a number line. $$ \left[-\frac{6}{5},-\frac{1}{2}\right] $$

simplify the expression. \(\frac{2 y^{2}-y-3}{2 y^{2}+y-1}\)

Rewrite the number without radicals or exponents.. $$ 32^{2 / 5} $$

Solve the given equation. $$ \frac{1}{3} k+1=\frac{1}{4} k-2 $$

Rewrite the number without using exponents. $$ -3^{-2}-\left(-\frac{2}{3}\right)^{2} $$

Factor out the greatest common factor. $$ 2 u\left(3 v^{2}+w\right)+5 v\left(3 v^{2}+w\right) $$

Classify the number as to type. (For example, \(\frac{1}{2}\) is rational and real, whereas \(\sqrt{5}\) is irrational and real.) $$ \frac{2}{\pi} $$

Evaluate the expression. $$ \left(-\frac{2}{3}\right)^{2}\left(-\frac{3}{4}\right)^{3} $$

Solve the equation by factoring, if required: $$ \frac{1}{4} x^{2}-x+1=0 $$

Show the interval on a number line. $$ (0, \infty) $$

Solve the given equation. $$ \frac{1}{5} p-3=-\frac{1}{3} p+5 $$

Rewrite the number without using exponents. $$ (0.02)^{2} $$

Factor out the greatest common factor. $$ (3 a+b)(2 c-d)+2 a(2 c-d)^{2} $$

Classify the number as to type. (For example, \(\frac{1}{2}\) is rational and real, whereas \(\sqrt{5}\) is irrational and real.) $$ 2 . \overline{421} $$

Evaluate the expression. $$ 2^{3} \cdot 2^{5} $$

Solve the equation by factoring, if required: $$ \frac{1}{2} a^{2}+a-12=0 $$

Show the interval on a number line. $$ (-\infty, 5] $$

simplify the expression. \(\frac{x^{3}+y^{3}}{x^{2}-x y+y^{2}}\)

Rewrite the number without radicals or exponents.. $$ -16^{3 / 2} $$

Solve the given equation. $$ 3.1 m+2=3-0.2 m $$

Rewrite the number without using exponents. $$ (-0.3)^{-2} $$

Factor out the greatest common factor. $$ 4 u v^{2}(2 u-v)+6 u^{2} v(v-2 u) $$

Evaluate the expression. $$ (-3)^{2} \cdot(-3)^{3} $$

Solve the equation by factoring, if required: $$ 2 m^{2}+m=6 $$

Find the values of \(x\) that satisfy the inequalities. $$ 2 x+4<8 $$

simplify the expression. \(\frac{x^{3}+y^{3}}{x^{2}-x y+y^{2}}\)

Rewrite the number without radicals or exponents.. $$ (-8)^{2 / 3} $$

Rewrite the number without using exponents. $$ 996^{0} $$

Indicate whether the statement is true or false. Every integer is a whole number.

Evaluate the expression. $$ (3 y)^{2}(3 y)^{3} $$

Solve the equation by factoring, if required: $$ 6 x^{2}=-5 x+6 $$

Find the values of \(x\) that satisfy the inequalities. $$ -6>4+5 x $$

simplify the expression. \(\frac{8 r^{3}-s^{3}}{2 r^{2}+r s-s^{2}}\)

Rewrite the number without radicals or exponents.. $$ (-32)^{3 / 5} $$

Solve the given equation. $$ \frac{1}{3} k+4=-2\left(k+\frac{1}{3}\right) $$

Rewrite the number without using exponents. $$ (18+25)^{0} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 6 x^{2}-x-1 $$