# The Factor Tree

**Example 12** Evaluate x + 3 if x = 4.

Replace x with 4. Add.

**Example 13** Evaluate 2 ( r – 5 ) if r = 3.

Replace r with 3. Simplify within the

parentheses by subtracting .

Multiply .

**Example 14** Evaluate 2 ( x + y ) if x = 4 and y = –1.

Replace x with 4 and y with –1. Simplify within

the parentheses by adding.

Multiply.

**Example 15** Evaluate
if
a = 2 and b = 8.

Replace a with 2 and b with 8.

The fraction bar serves as a grouping symbol .

Completely simplify the top and completely

simplify the bottom before dividing. Start by

adding on the top .

Divide.

**Example 16** Evaluate
if r = 16 and s = –5.

Replace r with 16 and x with –5. Evaluate the

root and exponent .

Multiply.

Subtract.

**Example 17** Evaluate

if
x = 5, y = 2 and z = 4.

Replace x with 5, y with 2, and z with 4.

The fraction bar serves as a grouping symbol.

Completely simplify the top and completely

simplify the bottom before dividing. Start by

evaluating the exponent.

Add or subtract in order from left to right.

Divide.

In application problems you may find it necessary to first write an algebraic
expression before

you can evaluate the expression. Recall from chapter 1 the words that represent
the different

mathematical operations .

**Example 18** Write an algebraic expression for each of the following. Use x
to

represent “a number”. Evaluate the expression when x = 2.

a) Twice a number

Words: | Twice | a number |

Algebraic 2 Expression : | 2 | • x |

Evaluate: |

b) Negative ten minus a number

Words: | Negative ten | minus | a number |

Algebraic Expression: | 10 | - | x |

Evaluate: |

c) Seven more than a number (the word than will reverse the order )

d) The product of a number and negative three

Words: | a number | The product of and |
negative hree |

Expression: | 3 | • | (-3) |

Evaluate: |

e) Eight times a number divided by four.

Words: | eight | times | a number | divided by | four |

Expression: | 8 | • | x | ÷ | 4 |

Evaluate: |

**In 21-25, find the average.**

21. Find the average of 12, 7, 0, 8, & 23. 22. Find the average of –5, –10, 18,
& –27.

23. Tommy’s allowance for the last 6 weeks was $10, $12, $15, $10, $8, and $11.
What was

his average weekly allowance?

24. Cali’s test scores in her English class were 84%, 73%, 98% and 90%. What was
her

average test score.

25. The morning temperatures for the last week were
. What

was the average morning temperature?

**In 26-33, evaluate the following expressions for x = 5, y = –2, and z = 3.**

**In 34-41, write an algebraic expression for the each of
the following. Use x, to represent “a**

number”. Evaluate the expression when x = 2.

34. The sum of three and a number.

35. The difference between a number

and twelve.

36. The quotient of six and a number.

37. The product of a number and

negative seven.

38. Fifteen less than a number.

39. Twenty-four decreased by twice a

number.

40. The square of a number increased by

negative seven.

41. The difference of three times a

number and four.

**2.4 REVIEW EXERCISES**

**In 1-4, use a factor tree to write the prime factorization of each number.**

**In 43-46, write an algebraic expression for the each of
the following. Use x, to represent “a**

number”. Evaluate the expression when x = 2.

43. The sum of a number and (–5).

44. 4 less than a number.

45. The quotient of (–8) and a number.

46. Twice a number increased by 3.

Prev | Next |