DAY 4
Factor and Long Division
Factor each expression completely.
1.
5 ( 2x + 1) + (5x − 6) ⋅2 ( 2x + 1) ⋅2
2
Step 1: Underline each term
(separated by + and –)
Step 2: Simplify each term
(do not distribute)
2.
3 ( 4x + 5) ⋅4 (5x + 1) + ( 4x + 5) ⋅2 (5x + 1) ⋅5
2
2
3
Step 3: Find the GCF
Step 4: Factor out the GCF
(divide and multiply)
Step 5: Simplify
Solve each equation for x.
3.
1 − ax = b, a ≠ 0
5.
A = P (1 + rt ) , solve for r.
4.
a b
+ = c, c ≠ 0
x x
6.
v = − gt + v 0 , solve for t
Note: When solving, use PEMDAS backwards = SADMEP!
LONG DIVISION
7.
Find the quotient and the remainder using long division.
(3x
3
)
− x 2 + x − 2 ÷ ( x + 2)
Step 1: Divide on the side.
Step 2: Write the quotient on top.
Step 3: Multiply.
Step 4: Subtract (change signs)
Step 5: Drop down next term.
Step 6: Then repeat!
The last number is the remainder.
The quotient is on top.
Answer =
8.
Check #3 using synthetic division.
quotient+ remainder
divisor
Step 1: Draw an “L”
Step 2: List the coefficients
(0 placeholders)
Step 3: Drop.
Step 4: Multiply and Add.
Step 5: Repeat Steps 2 and 3.
Last number is the remainder.
The quotient is on the top.
Answer =
quotient+ remainder
divisor
DAY 4
PRACTICE
Factor out the GCF.
1.
3x 2 (8x − 3) + x 3 ⋅8
3.
3x 2 (3x + 4 ) + x 3 ⋅2 (3x + 4 ) ⋅3
2
2.
4 ( x + 5) ( x − 1) + ( x + 5) ⋅2 ( x − 1)
3
2
4
Divide using long division =)
4.
(5x
4
5.
(x
− a5 ÷ (x − a )
5
)
(
− x2 + x − 2 ÷ x2 + 2
)
)