Chapter 1

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2 , by \(3,\) by \(5,\) by \(6,\) and by 10 . 84

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2 , by \(3,\) by \(5,\) by \(6,\) and by 10 . 96

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2 , by \(3,\) by \(5,\) by \(6,\) and by 10 . 896

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2 , by \(3,\) by \(5,\) by \(6,\) and by 10 . 942

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2 , by \(3,\) by \(5,\) by \(6,\) and by 10 . 22,335

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2 , by \(3,\) by \(5,\) by \(6,\) and by 10 . 39,075

In the following exercises, find the prime factorization. 86

In the following exercises, find the prime factorization. 78

In the following exercises, find the prime factorization. 455

In the following exercises, find the prime factorization. 432

In the following exercises, find the prime factorization. 627

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 8,12

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 12,16

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 28,40

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 84,90

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 55,88

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method. 60,72

In the following exercises, simplify each expression. $$ 2^{3}-12 \div(9-5) $$

In the following exercises, simplify each expression. $$ 3^{2}-18 \div(11-5) $$

In the following exercises, simplify each expression. $$ 2+8(6+1) $$

In the following exercises, simplify each expression. $$ 4+6(3+6) $$

In the following exercises, simplify each expression. $$ 20 \div 4+6(5-1) $$

In the following exercises, simplify each expression. $$ 33 \div 3+4(7-2) $$

In the following exercises, simplify each expression. $$ 3(1+9 \cdot 6)-4^{2} $$

In the following exercises, simplify each expression. $$ 5(2+8 \cdot 4)-7^{2} $$

In the following exercises, simplify each expression. $$ 2[1+3(10-2)] $$

In the following exercises, simplify each expression. $$ 5[2+4(3-2)] $$

In the following exercises, simplify each expression. $$ 8+2[7-2(5-3)]-3^{2} $$

In the following exercises, simplify each expression. $$ 10+3[6-2(4-2)]-2^{4} $$

In the following exercises, evaluate the following expressions. When \(x=2\), (a) \(x^{6}\) (b) \(4^{x}\) (c) \(2 x^{2}+3 x-7\)

In the following exercises, evaluate the following expressions. When \(x=3\), (a) \(x^{5}\) (b) \(5^{x}\) (c) \(3 x^{2}-4 x-8\)

In the following exercises, evaluate the following expressions. When \(x=4, y=1\) \(x^{2}+3 x y-7 y^{2}\)

In the following exercises, evaluate the following expressions. When \(x=3, y=2\) \(6 x^{2}+3 x y-9 y^{2}\)

In the following exercises, evaluate the following expressions. When \(x=10, y=7\) \((x-y)^{2}\)

In the following exercises, evaluate the following expressions. When \(a=3, b=8\) \(a^{2}+b^{2}\)

In the following exercises, simplify the following expressions by combining like terms. $$ 7 x+2+3 x+4 $$

In the following exercises, simplify the following expressions by combining like terms. $$ 8 y+5+2 y-4 $$

In the following exercises, simplify the following expressions by combining like terms. $$ 10 a+7+5 a-2+7 a-4 $$

In the following exercises, simplify the following expressions by combining like terms. $$ 7 c+4+6 c-3+9 c-1 $$

In the following exercises, simplify the following expressions by combining like terms. $$ 3 x^{2}+12 x+11+14 x^{2}+8 x+5 $$

In the following exercises, simplify the following expressions by combining like terms. $$ 5 b^{2}+9 b+10+2 b^{2}+3 b-4 $$

In the following exercises, translate the phrases into algebraic expressions. (a) the difference of \(5 x^{2}\) and \(6 x y\) (b) the quotient of \(6 y^{2}\) and \(5 x\) (c) Twenty-one more than \(y^{2}\) (d) \(6 x\) less than \(81 x^{2}\)

In the following exercises, translate the phrases into algebraic expressions. (@) the difference of \(17 x^{2}\) and \(5 x y\) (b) the quotient of \(8 y^{3}\) and \(3 x\) (C) Eighteen more than \(a^{2}\); (1) \(11 b\) less than \(100 b^{2}\)

In the following exercises, translate the phrases into algebraic expressions. (a) the sum of \(4 a b^{2}\) and \(3 a^{2} b\) (b) the product of \(4 y^{2}\) and \(5 x\) (c) Fifteen more than \(m\) (d) \(9 x\) less than \(121 x^{2}\)

In the following exercises, translate the phrases into algebraic expressions. (a) the sum of \(3 x^{2} y\) and \(7 x y^{2}\) (b) the product of \(6 x y^{2}\) and \(4 z\) (c) Twelve more than \(3 x^{2}\) (d) \(7 x^{2}\) less than \(63 x^{3}\)

In the following exercises, translate the phrases into algebraic expressions. (a) eight times the difference of \(y\) and nine (b) the difference of eight times \(y\) and 9

In the following exercises, translate the phrases into algebraic expressions. (a) seven times the difference of \(y\) and one (b) the difference of seven times \(y\) and 1

In the following exercises, translate the phrases into algebraic expressions. (a) five times the sum of \(3 x\) and \(y\) (b) the sum of five times \(3 x\) and \(y\)

In the following exercises, translate the phrases into algebraic expressions. (a) eleven times the sum of \(4 x^{2}\) and \(5 x\) (b) the sum of eleven times \(4 x^{2}\) and \(5 x\)

Eric has rock and country songs on his playlist. The number of rock songs is 14 more than twice the number of country songs. Let \(c\) represent the number of country songs. Write an expression for the number of rock songs.