Analytic Geometry
Name: ____________________________________
Unit 4
Study Guide
Date: _________________________
Period: ___________
Directions: Answer all of the questions, showing ALL of your work.
1. Classify the following polynomial by degree and number of terms (list both ways): (21𝑥 3 − 10𝑥 2 + 6𝑥 − 15)
2. Classify the following polynomial by degree and number of terms (list both ways): (8𝑥 2 𝑦 4 𝑧 − 2𝑥𝑦𝑧)
3. (3𝑥 3 + 2𝑥 4 − 3𝑥 2 ) + (2𝑥 2 + 𝑥 4 + 8𝑥 3 )
4. (𝑥 3 − 5𝑥 2 + 1) − (5𝑥 2 − 2 − 5𝑥 4 )
5. (3𝑥 + 6)2
6. (7 + 5𝑥)(7 − 5𝑥)
7. 8𝑥(2𝑥 − 7)
8. (6𝑥 + 2)(𝑥 + 4)
9. Simplify: √343𝑥 7
10. Simplify: √324𝑥 8
Analytic Geometry
Unit 4
Study Guide
11. Simplify √128 + √450 − 4√8
13. Simplify (4 - √3) (5 - √3 )
12. Simplify: √81 + √54 − √24
14. Evaluate: (4 − 3√2)(2 + √4)
15. Simplify: √7(−3√7 − 5√5)
16. “The sum of two rational numbers is….”
Explain your answer by using examples.
17. “The sum of two irrational numbers is….” Explain your answer by using examples.
18. Determine if the following statement is true or false. Explain your reasoning by using examples.
“Any decimal number is rational.”
19. Evaluate: (𝑥 4 )(𝑥 −2 )(𝑥 6 )
20. Evaluate: ((2𝑥 2 )2 )2
Analytic Geometry
Unit 4
Study Guide
21. Complete the table to make inferences about the product of rational and irrational numbers, then determine if the
statements are always true, sometimes true, or never true.
x
5
𝟏
𝟐
0
𝝅
−√𝟐
√𝟐
5
𝟏
𝟐
0
√𝟐
−√𝟐
𝝅
Response
1. The product of a rational
number and a rational
number is rational.
2. The product of a rational
number and an irrational
number is irrational.
3. The product of an irrational
number and an irrational
number is irrational.









Response Choices
Always true
Sometimes true
Never true
Always true
Sometimes true
Never true
Always true
Sometimes true
Never true
22. Determine whether each of the following mathematical statements is TRUE or FALSE. (YOU MUST SHOW
YOUR WORK)
TRUE
(8𝑥 6 + 𝑥 5 − 5𝑥 3 ) + (2𝑥 4 − 3𝑥 3 ) = 10𝑥 10 + 4𝑥 8 − 5𝑥 3
(2 − 4𝑥)(−3 − 2𝑥) = −6 − 8𝑥
(3𝑥 + 5)2 = 9𝑥 2 + 30𝑥 + 25
FALSE