Unit Summary 6
Class: Algebra 1
Unit 6: Polynomials – Chapter 9
I. Big Ideas:

Students will understand how to add, subtract, and multiply polynomials by using properties of
exponents and combining like terms.

Students will understand how polynomial expressions represent real-world situations.

Students will understand how to convert from the factored form of a polynomial to the standard form
of a polynomial and vice-versa.
II. Topics that will be covered:
1. Addition and subtraction of polynomials
2. Classify polynomials by number of terms
3. Classify polynomials by number of degree
4. Multiplication of polynomials
5. Special multiplications of polynomials
6. Factor by the GCF
7. Factor by grouping
8. Factor quadratic trinomials of the form x2 + bx + c
9. Factor quadratic trinomials of the form ax2 + bx + c
10. Solve equations by factoring
11. Graphing quadratics
III.
Essential Questions:

What are like terms?

What is the difference between classifying a polynomial by how many terms it has and its degree?

How is multiplying two polynomials different from adding them?

How do I identify the greatest common factor when given a polynomial?

How do I identify a difference of squares?

What does factoring a quadratic trinomial look like?

What is different about factoring a quadratic trinomial when “A” is not one?

How is solving by factoring different from just factoring?

What is the difference between factors and terms?
IV.
Sample questions to answer by the end of the unit:
Classify each polynomial by the number of terms.
1. 8xc9 – 6x5
2. 5x4y9d4
3. 7x4 + 3x2 – 12x
4. xy7 – 24xy5 + 32xy – 5
Classify each polynomial by its degree.
5. 8y
6. 3x2 + 6x – 2
7. 10x3 – 3x2 + 8x + 6
8. 6x - 19
Add or Subtract as indicated.
9. (5x4 – 2x2 + 6x - 9) + (2x4 + 5x2 – 7x + 12)
10. (4x3 + 7x2 - 5) – (2x3 – 3x2 + 5x – 9)
11. (8y3 + 7y2 – 2y + 10) + (5y – 3y2 – 7y3)
12. (4y5 – 6y3 + 8y – 5) – (7y3 + 5y – 8)
Multiply the following.
13. (x – 5)(2x + 7)
14. 3x(x – 2)(2x + 3)
15. (x + 3)2
16. (√2 + 6)(√2 – 6)
Factor each polynomial by grouping.
17. 5(x + 4) + y(x + 4)
18. ab + ac – 5b – 5c
19. 2y(y – z)2 – 5(y – z)2
20. 6m2 + 9m – 10m – 15
Factor each quadratic trinomial into two binomials.
21. c2 + 11c + 28
22. m2 – 14m – 32
23. x2 + x – 30
24. x2 + 14x + 48
25. 25x2 – 9
26. 81 – 4m2
Solve by factoring.
27. x2 + 9x + 20 = 0
28. x2 – 5x + 6 = 0
29. x2 + 13x = -42
30. x2 – 10x + 16 = 0
31. The height of a triangle is x – 3 units. The base of the triangle is 6x + 8 units. Express the area of the
triangle in terms of x.