1.1 Use the Language of Algebra

Is 5,625 divisible by ⓐ 2? ⓑ 3? ⓒ 5 or 10? ⓓ 6?

Is 4,962 divisible by ⓐ 2? ⓑ 3? ⓒ 5? ⓓ 6? ⓔ 10?

Is 3,765 divisible by ⓐ 2? ⓑ 3? ⓒ 5? ⓓ 6? ⓔ 10?

Find the prime factorization of $80 .$

Find the prime factorization of $60 .$

Find the LCM of 9 and 12 using the Prime Factors Method.

Find the LCM of 18 and 24 using the Prime Factors Method.

Simplify: $30 \div 5 + 10 \left(3 - 2\right) .$

Simplify: $70 \div 10 + 4 \left(6 - 2\right) .$

Simplify: $9 + 5^{3} - \left[4 \left(9 + 3\right)\right] .$

Simplify: $7^{2} - 2 \left[4 \left(5 + 1\right)\right] .$

Evaluate when $x = 3 ,$ ⓐ $x^{2}$ ⓑ $4^{x}$ ⓒ $3 x^{2} + 4 x + 1 .$

Evaluate when $x = 6 ,$ ⓐ $x^{3}$ ⓑ $2^{x}$ ⓒ $6 x^{2} - 4 x - 7 .$

Simplify: $3 x^{2} + 7 x + 9 + 7 x^{2} + 9 x + 8 .$

Simplify: $4 y^{2} + 5 y + 2 + 8 y^{2} + 4 y + 5 .$

Translate the English phrase into an algebraic expression:

ⓐ the difference of $14 x^{2}$ and 13 ⓑ the quotient of $12 x$ and 2 ⓒ 13 more than $z$
ⓓ 18 less than $8 x$

Translate the English phrase into an algebraic expression:

ⓐ the sum of $17 y^{2}$ and 19 ⓑ the product of $7$ and y ⓒ Eleven more than x ⓓ Fourteen less than 11a

Translate the English phrase into an algebraic expression:

ⓐ four times the sum of p and q
ⓑ the sum of four times p and q

Translate the English phrase into an algebraic expression:

ⓐ the difference of two times x and 8
ⓑ two times the difference of x and 8

The length of a rectangle is 14 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.

The length of a rectangle is 7 less than the width. Let w represent the width of the rectangle. Write an expression for the length of the rectangle.

The width of a rectangle is 6 less than the length. Let l represent the length of the rectangle. Write an expression for the width of the rectangle.

June has dimes and quarters in her purse. The number of dimes is seven less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.

Geoffrey has dimes and quarters in his pocket. The number of dimes is eight less than four times the number of quarters. Let q represent the number of quarters. Write an expression for the number of dimes.

Lauren has dimes and nickels in her purse. The number of dimes is three more than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.

Use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

84

Use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

896

Use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

22,335

Find the prime factorization.

86

Find the prime factorization.

455

Find the prime factorization.

432

Find the least common multiple of each pair of numbers using the prime factors method.

8, 12

Find the least common multiple of each pair of numbers using the prime factors method.

28, 40

Find the least common multiple of each pair of numbers using the prime factors method.

55, 88

Simplify each expression.

$2^{3} - 12 \div \left(9 - 5\right)$

Simplify each expression.

$2 + 8 \left(6 + 1\right)$

Simplify each expression.

$20 \div 4 + 6 \left(5 - 1\right)$

Simplify each expression.

$3 \left(1 + 9 \cdot 6\right) - 4^{2}$

Simplify each expression.

$2 \left[1 + 3 \left(10 - 2\right)\right]$

Simplify each expression.

$8 + 2 \left[7 - 2 \left(5 - 3\right)\right] - 3^{2}$

Evaluate the following expressions.

When $x = 2 ,$
ⓐ $x^{6}$
ⓑ $4^{x}$
ⓒ $2 x^{2} + 3 x - 7$

Evaluate the following expressions.

When $x = 4 , y = 1$
$x^{2} + 3 x y - 7 y^{2}$

Evaluate the following expressions.

When $x = 10 , y = 7$
$\left(x - y\right)^{2}$

Simplify the following expressions by combining like terms.

$7 x + 2 + 3 x + 4$

Simplify the following expressions by combining like terms.

$10 a + 7 + 5 a - 2 + 7 a - 4$

Simplify the following expressions by combining like terms.

$3 x^{2} + 12 x + 11 + 14 x^{2} + 8 x + 5$

Translate the phrases into algebraic expressions.

ⓐ the difference of $5 x^{2}$ and $6 x y$
ⓑ the quotient of $6 y^{2}$ and $5 x$
ⓒ Twenty-one more than $y^{2}$
ⓓ $6 x$ less than $81 x^{2}$

Translate the phrases into algebraic expressions.

ⓐ the sum of $4 a b^{2}$ and $3 a^{2} b$
ⓑ the product of $4 y^{2}$ and $5 x$
ⓒ Fifteen more than $m$
ⓓ $9 x$ less than $121 x^{2}$

Translate the phrases into algebraic expressions.

ⓐ eight times the difference of $y$ and nine
ⓑ the difference of eight times $y$ and 9

Translate the phrases into algebraic expressions.

ⓐ five times the sum of $3 x$ and $y$
ⓑ the sum of five times $3 x$ and $y$

Translate the phrases into algebraic expressions.

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.

Translate the phrases into algebraic expressions.

Greg has nickels and pennies in his pocket. The number of pennies is seven less than three times the number of nickels. Let n represent the number of nickels. Write an expression for the number of pennies.

Explain in your own words how to find the prime factorization of a composite number.

Explain how you identify the like terms in the expression $8 a^{2} + 4 a + 9 - a^{2} - 1 .$