MATH 130 · WEDNESDAY, SEPTEMBER 2, 2026
Show the steps.
Keep the factors.
A short review of algebra foundations,
then Quiz 1 in class.
RETRIEVE · WORK IN YOUR NOTES
Two quick checks
1 · Write the interval.
−2 < x ≤ 7
Which endpoint is included?
Explain the two symbols.
2 · Simplify. Assume x ≠ 0.
15x320x6
Use positive exponents
in the final answer.
CHECK YOUR REASONING
Two rules worth keeping straight
(−2, 7]
−2 is excluded: use (.
7 is included: use ].
x3 ÷ x6 = x3−6 = x−3
34x3
Subtract top exponent
minus bottom exponent.
FACTOR COMPLETELY
Take out the GCF first
9x2 − 36
= 9(x2 − 4)
= 9(x − 2)(x + 2)
Check: 9(x2 − 4) = 9x2 − 36.
First: what divides
every term?
Then: is the remaining expression a difference of squares?
Keep the 9 outside.
LEADING COEFFICIENT GREATER THAN 1
Use product ac and sum b
6x2 + 13x + 6
ac = 6 · 6 = 36 m + n = 13
9 and 4: 9 · 4 = 36, and 9 + 4 = 13.
6x2 + 9x + 4x + 6
The four-term line must equal the original expression.
THE SAME EXAMPLE · FINISH THE METHOD
Match the whole binomial
6x2 + 9x + 4x + 6
= 3x(2x + 3) + 2(2x + 3)
= (3x + 2)(2x + 3)
Check: 6x2 + 9x + 4x + 6 = 6x2 + 13x + 6.
The outside factors are 3x and 2.
The shared factor is the entire binomial 2x + 3.
YOUR TURN · WRITE EVERY LINE
GCF, then split and group
4x2 − 14x − 8
- Take out the GCF.
- Use the remaining quadratic to find ac and the pair.
- Split, group, factor, and expand to check.
CHECK YOUR WORK
Distribute the negative factor back
4x2 − 14x − 8 = 2(2x2 − 7x − 4)
ac = −8; use 1 and −8.
= 2[2x2 + x − 8x − 4]
= 2[x(2x + 1) − 4(2x + 1)]
= 2(x − 4)(2x + 1)
Check: 2(2x2 + x − 8x − 4) = 4x2 − 14x − 8.
FACTOR BEFORE CANCELING
Restrictions survive cancellation
x2 − 9x2 + x − 12 = (x − 3)(x + 3)(x − 3)(x + 4)
From the original denominator: x ≠ 3, −4.
= x + 3x + 4, x ≠ 3, −4
Cancel a whole factor. Keep both original restrictions.
BEFORE YOU FINISH A PROBLEM
Make the reasoning visible
- Does each line still equal the original expression?
- For grouping: did you show the pair and the split?
- Did you keep the GCF and check by expanding?
- For a fraction: did you keep every original restriction?
QUIZ 1 · IN CLASS
One page. Show your work.
6 questions · 100 points · 25 minutes
- Write your name in the top-right box.
- Work inside each question’s area, beside its expression.
- Follow the announced resource rules.
- Wait for the instruction to begin.
QUIZ 1
Time remaining
25:00
Work independently. Show your reasoning.
Keep your work inside the question areas.
QUIZ 1 · SUBMIT
Please stop writing.
Check that your name is on the page.
Hand in your quiz as directed.
Make sure your page has been collected before leaving.