Factoring
Factor:
6x+36
Answer: 6(x + 6)
Help: Factors of 6: 1 & 6, 2 & 3
Factors of 36: 1 & 36, 2 & 18, 3 & 12, 4 & 9, 6 & 6
Biggest number on both lists: 6
Divide 6x + 36 by 6.
Distribute:
4(x-9)
4x-36
Times 4 by x. Times 4 by -9
Combine the Like Terms:
4a + 2a
6a
Because both terms have the same variable, you just add the coefficients 4 + 2
If x=4, y=-7, and z=3
7x - 7y
77
Replace x with 4 and y with -7
7(4) - 7(-7)
z means nothing because it's not in the expression.
4(3x + 2) + 5
12x + 13
4*3x = 12x
4 * 2 = 8
8 + 5 = 13
What is the definition for a Variable?
A symbol used in place of a number
If 8 bottles of apple juice cost $24, how much does one bottle of apple juice cost?
$3
24/8
Factor:
8x-32
8(x-4)
Factors of 8: 1 & 8, 2 & 4
Factors of 32: 1 & 32, 2 & 16, 4 & 8
Biggest number on both lists (GCF): 8
Divide 8x - 32 by 8
Distribute:
-1/3(12x-24)
-4x+8
Times -1/3 by 12
Times -1/3 by -24
Pro tip: Times by 1/3 is the same as dividing by 3.
Combine the Like Terms:
5.6w-9.6w+3
-4w+3
5.6 - 9.6 = -4. (different signs subtract)
3 just keeps hanging out.
If x=4, y=-7, and z=3
1/7(y+z)
-4/7
Replace y with -7 and z with 3
1/7(-7+3)
1/7(-4)
-3(2x - 4) + 6
-6x + 18
-3 * 2x = -6x
-3 * -4 = 12
12 + 6 = 18
What is the definition for an expression?
A number sentence without an equal sign.
If 12 bottles of Orange Juice cost $48, how much will 4 bottles of orange juice cost?
$16
48 /12 = 4
4 * 4 = 16
Factor:
12x+48
Factors of 12: 1 & 12, 2 & 6, 3 & 4
Factors of 48: 1 & 48, 2 & 24, 3 & 16, 4 & 12, 6 & 8
GCF: 12
Divide 12x + 48 by 12
Distribute:
11(4x-7y)
44x-77y
Times 11 by 4
times 11 by -7
Combine the Like Terms:
7r +3 -3r - 4+2
4r +1
7r - 3r = 4r
3 - 4 + 2 = 1
if x=4, y=-7, and z=3
xz+y
5
Replace each variable with the value it is equal to.
4*3 + -7
2 - (3x + 4)
-3x - 2
If there's no number in front of the parentheses, it is a 1.
-1 * 3x = -3x
-1 * 4 = -4
2 + -4 = -2
What is the definition for a term?
Parts of an expressions separated by a +, -, or =.
8 - (-3)
11
minus a negative is a plus
8 + 3
Factor:
-16x-20
-4(4x+5)
Factors of 16: 1 & 16, 2 & 8, 4 & 4
Factors of 20: 1 & 20, 2 & 10, 4 & 5
GCF is 4
Divide both sides by -4 You divide by a negative because the variable is negative.
Distribute:
-8(4x-8)
-32x + 64
times -8 by 4
times -8 by -8
Combine the Like Terms:
42x-10y+x-10y
43x-20y
42x + x = 43x (x IS 1x)
-10y - 10y = -20y
If x=4, y=-7, and z=3
-4x+5z+2y
-15
Replace each variable with the value it is equal to
-4*4 + 5*3 + 2*-7
-4(3a + 8) + 5a
-7a - 32
-4 * 3a = -12a
-4 * 8 = -32
-12a + 5a = -7a
What is the definition for constant?
-6 + (-3)(4)
-18
-3 * 4 = -12
-6 + -12 They are both negative so add them.
Factor:
- 35x + 42
-7(5x - 6y)
Factors of 35: 1 & 35, 5 & 7
Factors of 42: 1 & 42, 2 & 21, 3 & 14, 6 & 7
GCF: 7
Divide -35x + 42 by -7 because the variable is negative.
Distribute:
-2(x+5y-9)
-2x-10y+18
times -2 by x
times -2 by 5
times -2 by -9
Combine the Like Terms:
1/3x+5-3/7x+6
-2/21x+11
1/3 - 3/7 = -2/21
5 + 6 =11
if x=4, y=-9, and z=3
(15x)/(6z-5y)
60/63
Replace each variable with the value it is equal to
15 * 4 = 60
6 * 3 - 5* -9 = 18 + 45 = 63
8 - 3(2x + 4) + 5x
-1x - 4
-3 * 2x = -6x
-3 * 4 = -12
-6x + 5x + -1x
8 + (-12) = -4
What is the definition for a coefficient?
The number in front of the variable.
A scuba diver was 342 feet below the surface. A hiker was climbing a nearby mountain 524 feet above the surface. How many feet apart are they?
866 feet
524 - (-342)
minus a negative is plus
524 + 342
This is a level 4 Challenge Problem. See if you can figure it out.
Factor:
12x-24y+18
6(2x-4y+3)
Factors of 12: 1 & 12, 2 & 6, 3 & 4
Factors of 24: 1 & 24, 2 & 12, 3 & 8, 4 & 6
Factors of 18: 1 & 18, 2 & 9, 3 & 6
Biggest number on all lists: 6
Divide 12x - 24y + 18 by 6
Distribute:
4(6x-4y-2z)
24x-16y-8z
times 4 by 6x
times 4 by -4y
times 4 by -2z
Combine the Like Terms:
-1/3(3x-12+9x-5)
-4x + 5 2/3
-1/3 * 3x = -1x
-1/3 * -12 = 4
-1/3 * 9x = -3x
-1/3 * -5 = 5/3
-1x + -3x = -4x
4 + 5/3 = 5 2/3
if x=4, y=-7, and z=3
5x^2+3z+4
93
5 * 4 * 4 + 3 * 3 + 4
2/3(9x - 3) + 3/4(-8x+12)
7
2/3 * 9x = 6x
2/3 * -3 = -2
3/4 * -8x = -6x
3/4 * 12 = 9
6x - 6x = 0
9 - 2 = 7
What is an algebraic expression
A number sentence with a variable and NO equals sign
While playing a board game, Cecilia had to move back 3 spaces 9 times. What integer represents Cecilia's movement on the board for those 9 turns?
-27
Move backward is negative
-3 * 9 = -27