
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.
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 x
2
+ bx + c
9.
Factor quadratic trinomials of the form ax 2 + bx + c
10.
Solve equations by factoring

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?

Classify each polynomial by the number of terms.
1. 8xc
9
– 6x
5
2. 5x
4 y
9 d
4
3. 7x
4
+ 3x
2
– 12x
Classify each polynomial by its degree.
5. 8y
7. 10x 3 – 3x 2 + 8x + 6
4. xy
6. 3x
7
2
– 24xy
5
+ 32xy – 5
+ 6x – 2
8. 6x - 19
Add or Subtract as indicated.
9. (5x
4
– 2x
2
+ 6x - 9) + (2x
4
+ 5x
2
– 7x + 12)
10. (4x 3 + 7x 2 - 5) – (2x 3 – 3x 2 + 5x – 9)
11. (8y
3
+ 7y
2
– 2y + 10) + (5y – 3y
2
– 7y
3
)
12. (4y 5 – 6y 3 + 8y – 5) – (7y 3 + 5y – 8)
Multiply the following.
13. (x – 5)(6x + 7)
15. (x – 5)
2
14. 4x(x – 2)(2x + 3)
16. (√3 + 6)(√3 – 6)

Factor each polynomial by grouping.
17. 5(x + 4) + y(x + 4)
19. 2y(y – z)
2
– 5(y – z)
2
18. ab + ac – 5b – 5c
20. 6m
2
+ 9m – 10m – 15
Factor each quadratic trinomial into two binomials. If it cannot be factored, write not factorable.
21. c
2
+ 11c + 28 22. m
2
– 14m – 32
23. x 2 + x – 30 24. x 2 + 14x + 48
25. 25x
2
– 9 26. 81 – 4m
2
27. 9x 2 – 12 x + 4
Solve by factoring.
29. x
2
+ 9x + 20 = 0
28. 3x
30. x
2
2 – 17x - 28
– 5x + 6 = 0

31. x 2 + 13x = -42 32. x 2 – 10x + 16 = 0
33. 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.