Polynomial Exit Ticket Answer Key
Teacher Resource Algebra • Unit 2
Polynomial Exit Tickets • Answer Key
Official Solutions
Days 1 & 2 • Oct 2–8, 2024
Day 1 — Exit Ticket Polynomial Vocabulary & Standard Form
October 2–4, 2024
1 Degree & Number of Terms
Classify the polynomial:
\(-6x^3 + 2x^2 + 8x - 5\)
Highest exponent: 3 (Cubic)
Number of terms: 4 terms
Final Answer
Cubic polynomial with 4 terms
(or 4-term cubic polynomial)
2 Standard Form
Simplify and write in standard form:
\(x^3 + 4x^2 - 6x + 2 - 6x^2 + 10x - 2\)
Combine Like Terms:
• \(x^3\)
• \(4x^2 - 6x^2 = -2x^2\)
• \(-6x + 10x = +4x\)
• \(+2 - 2 = 0\)
Final Answer
\(x^3 - 2x^2 + 4x\)
Day 2 — Exit Ticket Adding & Subtracting Polynomials
October 7–8, 2024
Add or subtract each polynomial. Write your answer in standard form.
3 Addition of Polynomials
Problem & Steps
\((4y^4 + 10y^3 - 6) + (3y^4 - 7y^3 + 2y)\)
\(= (4y^4 + 3y^4) + (10y^3 - 7y^3) + 2y - 6\)
Combine like degrees in descending order
Final Answer
\(7y^4 + 3y^3 + 2y - 6\)
4 Subtraction of Polynomials (Distribute Negative)
Watch Signs
\((15x^3 - 3x^2 - 1) - (10x^3 - 4x^2 + 14)\)
\(= 15x^3 - 3x^2 - 1 - 10x^3 + 4x^2 - 14\)
\(= (15-10)x^3 + (-3+4)x^2 + (-1-14)\)
Final Answer
\(5x^3 + x^2 - 15\)
5 Rational Polynomial Expressions (Common Denominator)
\(\text{LCD} = 10\)
\(\left(\frac{x+1}{5}\right) + \left(\frac{x-1}{10}\right)\)
\(= \frac{2(x+1)}{10} + \frac{x-1}{10} = \frac{2x + 2 + x - 1}{10}\)
\(= \frac{3x + 1}{10}\)
Final Answer
\(\frac{3x + 1}{10}\)
or \(\frac{3}{10}x + \frac{1}{10}\)
Unit 2 Polynomials Exit Ticket • Teacher Answer Key Page 1 of 2
Teacher Resource Algebra • Unit 2
Polynomial Exit Tickets • Answer Key
Official Solutions
Days 3 & 4 • Oct 9–16, 2024
Day 3 — Exit Ticket Function Operations: Tables & Rules
October 9–10, 2024
6 Find the function values for \(h(x) = (f - g)(x)\) in the table:
Key Row Highlighted
| \(x\) | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|---|
| \(f(x) = 12x^2 - 5x + 1\) | 124 | 59 | 18 | 1 | 8 | 39 | 94 |
| \(g(x) = 3x + 7\) | -2 | 1 | 4 | 7 | 10 | 13 | 16 |
| \(h(x) = (f - g)(x)\) | 126 | 58 | 14 | -6 | -2 | 26 | 78 |
Calculation note: For each column, subtract \(f(x) - g(x)\). Ex: \(124 - (-2) = 126\), \(1 - 7 = -6\).
7 Rule for \(h(x) = (f - g)(x)\)
\((f - g)(x) = f(x) - g(x)\)
\(= (12x^2 - 5x + 1) - (3x + 7)\)
\(= 12x^2 - 5x + 1 - 3x - 7\)
Final Function Rule
\(h(x) = 12x^2 - 8x - 6\)
8 Rule for \(h(x) = (f + g)(x)\)
\((f + g)(x) = f(x) + g(x)\)
\(= (12x^2 - 5x + 1) + (3x + 7)\)
\(= 12x^2 + (-5x + 3x) + (1 + 7)\)
Final Function Rule
\(h(x) = 12x^2 - 2x + 8\)
Day 4 — Exit Ticket Multiplying Binomials & Area Applications
October 15–16, 2024
9 Simplify \((2x - 6)(x + 11)\)
FOIL / Distributive Method:
• First: \(2x \cdot x = 2x^2\)
• Outer: \(2x \cdot 11 = +22x\)
• Inner: \(-6 \cdot x = -6x\)
• Last: \(-6 \cdot 11 = -66\)
Combine middle terms: \(22x - 6x = +16x\)
Final Answer
\(2x^2 + 16x - 66\)
10 Area of the Rectangle
\(x + 7\)
\(x - 11\)
\(\text{Area} = l \times w\)
\(\text{Area} = (x + 7)(x - 11)\)
\(= x^2 - 11x + 7x - 77\)
Final Answer
\(x^2 - 4x - 77\)
(square units)
Unit 2 Polynomials Exit Ticket • Teacher Answer Key Page 2 of 2
