A.2
The student will perform operations on polynomials, including
a) applying the laws of exponents to perform operations on expressions;
b) adding, subtracting, multiplying, and dividing polynomials; and
c) factoring completely first- and second-degree binomials and trinomials
in one or two variables. Graphing calculators will be used as a tool for
factoring and for confirming algebraic factorizations.
Simplify the following expressions
1. (3x3 +2x2 -4x+2) + (2x3 - x2 – 4x +1)
2. (-6x3 -3x2 +2) + (-x3 +3x2 – 2x +8)
3. (2x3 -9x2 +9x+6) + (6x3 – 8x +4)
4. (3x4 -2x3 + 2x2 -4x+2) + (2x3 - x2 – 4x +1)
5. (2x3 +4x2 -4x+9) - (5x3 - 2x2 – 4x +1)
6. (2x4 -7x2 - 5x+2) - (-3x3 +6x2 – 7x +8)
7. (3x5 +8x2 –x - 10) - (-10x3 - 7x2 – 9x -17)
8. (7x5 -5x3 -4x2+7) - (-7x5 -9x3 + 6x +9)
Simplify the follow expressions
9. 2x2 ( 9x7 -6x-2)
10.
-3x4(-2x2+10x-9)
11.
-2x2y2(9x2y – 4xy +2)
12.
-2x2 ( 10x3 +2x-9)
13.
-4xy( 6x2y – 9xy2+2)
14.
7x2y3 (-2x3y2 + 10xy -9)
Find the product of the following
15.
(x-9)(x+2)
16.
(2x+8)(-3x+2)
17.
(3x-4)(2x-9)
18.
(-7x2 +3)(2x2-3)
19.
(9x-9)(9x+9)
20.
(4x-4)(-2x-2)
21.
(-6x+6)(-6x-6)
22.
(3x2-9)(4x2+2)
Simplify:
23.
(3x-2)2 (-4x-3)
24.
25.
26.
27.
28.
(5x)2(9x-4)
Factor each of the following completely
29.
x2 +3x + 2
30.
x2 +7x + 6
31.
x2 -6x + 8
32.
x2 +2x – 48
33.
x2 -9x + 18
34.
x2 -49
35.
x2 - 64
36.
x2 – y2
37.
2x2 -5x – 3
38.
3x2 -7x -6
39.
9x2 – 39x -30
40.
6x2 +3x – 3
41.
3x2 +7x -2