Contents

Preface
1Foundations
- Introduction
- 1.1Use the Language of Algebra
- 1.2Integers
- 1.3Fractions
- 1.4Decimals
- 1.5Properties of Real Numbers
- Chapter Review
  Key Terms
  Key Concepts
- Exercises
  Review Exercises
  Practice Test
2Solving Linear Equations
3Graphs and Functions
4Systems of Linear Equations
5Polynomials and Polynomial Functions
6Factoring
7Rational Expressions and Functions
8Roots and Radicals
9Quadratic Equations and Functions
10Exponential and Logarithmic Functions
11Conics
12Sequences, Series and Binomial Theorem
- Introduction
- 12.1Sequences
- 12.2Arithmetic Sequences
- 12.3Geometric Sequences and Series
- 12.4Binomial Theorem
- Chapter Review
  Key Terms
Answer Key
Index

Practice Test

487.

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

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

488.

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

489.

$(10 x^{2} - 3 x + 5) - (4 x^{2} - 6) (10 x^{2} - 3 x + 5) - (4 x^{2} - 6)$

490.

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

491.

$x^{−3} x^{4} x^{−3} x^{4}$

492.

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

493.

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

494.

$4^{−1} 4^{−1}$

495.

${(2 y)}^{−3} {(2 y)}^{−3}$

496.

$p^{−3} \cdot p^{−8} p^{−3} \cdot p^{−8}$

497.

$\frac{x^{4}}{x^{−5}} \frac{x^{4}}{x^{−5}}$

498.

${(3 x^{−3})}^{2} {(3 x^{−3})}^{2}$

499.

$\frac{24 r^{3} s}{6 r^{2} s^{7}} \frac{24 r^{3} s}{6 r^{2} s^{7}}$

500.

${(\frac{x^{4} y^{9}}{x^{−3}})}^{2} {(\frac{x^{4} y^{9}}{x^{−3}})}^{2}$

501.

$(8 x y^{3}) (−6 x^{4} y^{6}) (8 x y^{3}) (−6 x^{4} y^{6})$

502.

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

503.

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

504.

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

505.

${(4 x - 3)}^{2} {(4 x - 3)}^{2}$

506.

$(5 x + 2 y) (5 x - 2 y) (5 x + 2 y) (5 x - 2 y)$

507.

$(15 x y^{3} - 35 x^{2} y) \div 5 x y (15 x y^{3} - 35 x^{2} y) \div 5 x y$

508.

$(3 x^{3} - 10 x^{2} + 7 x + 10) \div (3 x + 2) (3 x^{3} - 10 x^{2} + 7 x + 10) \div (3 x + 2)$

509.

Use the Factor Theorem to determine if $x + 3 x + 3$ a factor of $x^{3} + 8 x^{2} + 21 x + 18 . x^{3} + 8 x^{2} + 21 x + 18 .$

510.

ⓐ Convert 112,000 to scientific notation. ⓑ Convert $5.25 \times 10^{−4} 5.25$ to decimal form.

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

511.

$(2.4 \times 10^{8}) (2 \times 10^{−5}) (2.4) (2)$

512.

$\frac{9 \times 10^{4}}{3 \times 10^{−1}} \frac{9}{3}$

513.

For the function $f (x) = 6 x^{2} - 3 x - 9 f (x) = 6 x^{2} - 3 x - 9$ find:
ⓐ $f (3) f (3)$ ⓑ $f (−2) f (−2)$ ⓒ $f (0) f (0)$

514.

For $f (x) = 2 x^{2} - 3 x - 5 f (x) = 2 x^{2} - 3 x - 5$ and $g (x) = 3 x^{2} - 4 x + 1, g (x) = 3 x^{2} - 4 x + 1,$ find
ⓐ $(f + g) (x) (f + g) (x)$ ⓑ $(f + g) (1) (f + g) (1)$
ⓒ $(f - g) (x) (f - g) (x)$ ⓓ $(f - g) (−2) (f - g) (−2)$

515.

For functions
$f (x) = 3 x^{2} - 23 x - 36 f (x) = 3 x^{2} - 23 x - 36$ and
$g (x) = x - 9, g (x) = x - 9,$ find
ⓐ $(\frac{f}{g}) (x) (\frac{f}{g}) (x)$ ⓑ $(\frac{f}{g}) (3) (\frac{f}{g}) (3)$

516.

A hiker drops a pebble from a bridge 240 feet above a canyon. The function $h (t) = −16 t^{2} + 240 h (t) = −16 t^{2} + 240$ gives the height of the pebble $t t$ seconds after it was dropped. Find the height when $t = 3 . t = 3 .$