Mastery Learning Algebra 1
Exponents, GCF, Simplify, Factor
Exponents
Adding/Subtracting: Only add/sub. coefficients
of like terms. EXPONENTS DO NOT CHANGE!
Example: 3x7-2x3+5x7+x3
7
Add the numbers in front of x : 3+5=8
Add the numbers in front of x3 : -2+1=-1
ANSWER: 8x7- x3
Multiplying: Multiply coefficients, add x
exponents
 Ex: 5 y  3 y  15 y
Dividing: Divide coefficients, subtract exponents
and put the exponent whereever the larger
exponent was: (Big – Little)
2
3.
7
2 3
Ex:  21a b
7ab 6

1.
2.
5
3
Answer:  3a
b3
4
5
D. 7x2 – 3x – 3
2
2. Simplify (3c d )(5c d )
A. -15c15d8
B. -15c8d C. -15c8d6
2
3. Simplify
D. -8c8d8
5 4
60x y z
4 x 4 y 2 z
A. -15x2y3z3
3 4
3 4
B.  15 y z C.  56 y z
x2
2
x
3 3
D.  15 y z
2
x2
3 2
4. Simplify (6b c )

A. 12b4c6
B.36b4c6 C. 12b4c5
2 5
5. Simplify.  8r  r t 
D. 36b4c5
0
 1 
 3s  t 
A.
Divide -21 and 7=-3
a : subtract the exponents 2-1=1 so a1
goes on top
b : subtract the exponents 6-3=3
So b3 goes on bottom
8r
3s
6
B. 8t
4 2
6. Simplify  2b n 
3 

 3a
12
C. 5t6
D. 0
3
6
3

7 5
B. 8b n
A. 8b n
27 a 9
27 a
6
7
C. 2b n
3a 6
5
12 6
D. 2b n
3a 9
7. Simplify  p q 
 6 
3
Zero: Anything to the zero power equals 1
2
 p q 
3
B. p
3
q
3
A. p
has the power of zero.
8. Find the perimeter of a triangle whose sides are
(3x2 + 5);(5x – 2); and (6x2 + 5x)
A. 9x2 + 10x + 3
B. 19x2 + 3
C. 9x4 + 10x2 – 3
D. 7x4 + 10x - 3
 3x y  3 y Note that only x is
raised to the zero power, so only
0
2
2
x 0  1 the rest of the factor remains.
q
C.
3
D. p
(2a 3bc 8 ) 0  1 The whole quantity


You Try:
1. Simplify: 7x2 – 5x – 3 + 2x
A. 7x2 + 3x – 3 B. x4 C. -3
1
p q3
3
q2
Distribute: Always distribute first, then combine 9. Simplify (2x  5)(2x  3)
like terms.
A. 4x2 – 15
B. 4x2 – 4x – 15
2
2

Ex: 2 x(3  4 x)  x(3x  1) Multiply
C. 4x + 4x – 15
D. 8x - 15
what is on the outside of the parenthesis to
10. Simplify (3x2 + 5x + 1) – (7x2 – 2)
each term on the inside of the parenthesis.
2
B. -4x2 + 5x -1
6x-8x2- 3x3 + 5x Then combine like terms. A. -4x + 5x + 3
C. x2 – 1
D. x2 + 3
The only like terms in this example are 6x
2
3
2
and –x. ANSWER: -3x – 8x + 5x
11. Simplify (x  2)(3x  x  4)
3
2
A. 3x – 7x + 6x – 8
B. 3x3 – 6x2 + 6x + 4
30a 6b 3 12a 2b 4 30a 6 b 3 12a 2 b 4
Ex:
=

C. 3x3 + 7x2 – 6x – 8
D. 2x3 – 8
6ab
6ab
6ab

= ANSWER:5a5b2 – 2ab3
Multiply: If given two polynomials, use FOIL or
the box method to multiply.

Ex:
(2 x  1)( x 2  3x  5) box
x2
2x
+1
2x 3
x2
-3x
+5
 6x 2
 3x
10 x
5
(continue on next page)
12.
 Find the perimeter of a rectangle if the width is
(2x – 4) and the width is (5x + 1).
A. 7x – 3
B. 7x + 3
C. 14x – 6
D. 14x + 6
13. Find the area of a triangle if the base is
(2x – 4) and the height is (x + 6)
A. x2 + 4x – 12
B. 2x2 + 8x – 24
2
C. 2x – 8x – 24
D. 3x + 2
Mastery Learning Algebra 1
Exponents, GCF, Simplify, Factor
Rewrite the contents of the box and then
4 xy2  6 xy  8x 2 y
146.
14.
Simplify
combine like terms.
2 xy
2 x 3  6 x 2  10 x  x 2  3x  5 Like
A. 2xy – 3 + 4x
B. 2y – 3 + 4x
2
2
D. 2xy – 3 + 4x2
terms in this example are  6x and x as C. 2y – 3 + 4xy
well as 10 x and  3x .
15. Find the area of a square whose side is 3x4
3
2
ANSWER: 2 x  5 x  7 x  5
A. 12x4
B.9x16
C. 12x6
D. 9x8
GCF
CALCULATOR: [MATH]->NUM 9: gcd(
Type 2 numbers with ‘,’ between.
If there are more than two then pair each
number together. Then find the greatest
common factor between your answers.
 Ex: Find the GCF of 12, 18, 36
gcd(12, 18)=6
gcd( 12, 36) =12
gcd( 18, 36)= 18 so GCF = 6
Variables: Take the smallest exponent of each
variable.

Ex:
a12bc 4 , a 6 b 3 c 2 , a 9 b 5 c 6
6
ANSWER: a bc
2
158.
Factor Ax  Bx  C
1.
When factoring a trinomial, factor out
any GCF(number and/or variable) between
all three terms.
2.
Multiply the coefficient of the first
term by the last term.
3.
Find the factors of this multiplied
number that add to the middle term
CALCULATOR STEPS: Go to y=
Y1= AC Y2= B - x
2
x
6
4
16. Find the GCF: 63x y & 18 x
A. 3x6y9
B. 9x6y9
C. 3x3y4
3
y9
D. 9x3y4
17. Find the GCF: 60r3s2 & 15r2s & 27rs3
A.5r3s3
B. 5r3s3
C. 3rs
D. 3r3s3
18. Find the GCF: 12x2y4 & 60x3y6 & 36x4y3z
A. 12x2y3
B. 12x4y6z C. 6x2y3 D. 12x4y6z
<Another way to see if something is a factor is to do 17
STO X ENTER. Then divide the (problem) by each
(factor). If you get an integer then it’s probably a
factor>
19. The area of a rectangle is given by the expression
of x - 5x - 6. The length and width only have integral
coefficients. Which of the following could represent
the length of the rectangle?
A. x – 6
B. x – 2
C. x – 3
D. x – 1
20. Factor completely:
A. a(2a – 7)(a + 3)
C. a(a + 3)(a – 7)
2a 3  a 2  21a
B. a(2a+7)(a – 3)
D. a(a – 3)(a + 7)
[2nd] [Graph] (Table) Look where Y1 and Y2 are
1 21. Which is a factor of 10x2 + 29x - 21?
the same. Let Bx be ‘x’x and ‘Y1’x
A. 5x + 3
B. 5x – 3
4. Rewrite as Ax2 + xx + Y1x + C.
C.
2x
–
7
D. 10x + 7
5. Solve by grouping.
* Example: 2 x  5 x  3 x
3
2
1. x(2 x  5 x  3)
2. Factors of 6 that add to 5
3. 1, 6
2, 3 **
4. (2x2 + 2x) + (3x + 3)
5. 2x(x + 1) + 3(x + 1)
(2x + 3)(x + 1)
5. ANSWER: x( x  1)( 2 x  3)
2
22. Factor completely: 4 x  24 x
A. (2x – 10)(2x – 2) B. 4(x – 5)(x – 1)
C. 4(2x -10)(x – 1) D. (2x – 10)(x + 1)
2

 20