Linear Equations
Polynomials
100
3t + 7 = 22
What is
subtract 7 from both sides
3t = 15 (divide both sides by 3)
t = 5
100
(x+3)(x+4)
What is FOIL
x2 + 4x + 3x + 12
x2 + 7x + 12
200
22 – 6/7 x > 16
What is
add 6/7 x to both sides
subtract 16 from both sides
6 > 6/7x (divide both sides by 6/7)
6/(6/7) = 6/1 x 7/6 = 7
x > 7
200
Which of the following is a factor of both x2 – x – 6 and x2 – 5x + 6?
Reverse FOIL both expressions
(x )(x )
-6 (factors that add to -1, -3, 2)
(x-3)(x+2)
(x )(x )
6 (Factors of 6 that add to negative 5, -2, -3)
(x - 2)(x-3)
(x-3) is common to both
300
2x – 3(x + 4) = –5, then x =
What is 2x - 3x - 12 = -5
-x - 12 = -5 (add 12 to both sides)
-x = 7
x = -7
300
(10x6 + 8x4 )/ 2x2
What is 5x4 + 4x2
400
Solve system of equations
3x - y = 7
2x + 3y = 1
What is
1. Solve for x (eliminate y)
2. Multiply top equation by 3: 9x - 3y = 21
3. Add new top equation to bottom
9x - 3y = 21
2x + 3y = 1 (Y cancels)
11x = 22 (Divide by 11)
x = 2
4. Plug x=2 into ORIGINAL top equation
3(2) - y = 7
6 - y = 7
-y = 1
y = -1
Solution is (2, -1)
400
A rectangular yard has area 96 square feet. If the width of the yard is 4 feet less than the length, what is the perimeter, in feet, of the yard?
Draw a picture
L = length
Width = L -4
Area = LxW = 96
96 = L(L-4)
96 = L2 - 4L
L2 - 4L - 96 = 0
(L-12)(L+8) = 0
Set each equal to 0 and solve for L
L = 12 and L = -8
L = 12 feet so width = 12 - 4 feet = 8 feet
500
What is the radius of a circle with an area of 25π in2?
A = pi (radius2)
A = 25(pi)
25 = radius2 (take square root of both sides)
radius = 5 inches
500
We will solve together