Unit 10 · 9th Grade Mathematics
Polynomials.
Naming, adding, subtracting, multiplying polynomials, and factoring techniques.
Topic A: Polynomial Operations
Lessons 1–4 · Adding, subtracting, and multiplying polynomials.
01–02 — Lessons 1–2
Adding & Subtracting Polynomials
- Polynomial: sum of terms with non-negative integer exponents.
- Named by degree: linear (1), quadratic (2), cubic (3).
- Named by terms: monomial (1), binomial (2), trinomial (3).
- Add: combine like terms.
- Subtract: distribute the negative, then combine like terms.
(3x² + 2x − 1) − (x² − 5x + 3) = 3x² + 2x − 1 − x² + 5x − 3 = 2x² + 7x − 4
Practice — Lessons 1–2
Q1 · Short Answer
Add: (4x² − 3x + 2) + (−2x² + 5x − 7). What is the coefficient of x?
Q2 · Multiple Choice
What is a trinomial?
03–04 — Lessons 3–4
Multiplying Polynomials
- Use the distributive property. For binomials: FOIL (First, Outer, Inner, Last).
- (a+b)(c+d) = ac + ad + bc + bd
- Degree of product = sum of degrees.
- Perfect square: (a+b)² = a² + 2ab + b².
- Difference of squares: (a+b)(a−b) = a² − b².
(2x + 3)(x − 4) = 2x² − 8x + 3x − 12 = 2x² − 5x − 12
Practice — Lessons 3–4
Q3 · Short Answer
Expand (x + 5)². What is the middle term?
Q4 · Multiple Choice
(x + 7)(x − 7) equals:
Topic B: Factoring
Lessons 5–8 · GCF, trinomial factoring, and special patterns.
05–08 — Lessons 5–8
Factoring Techniques
- Always factor out the GCF first.
- Trinomial (a=1): find two numbers that multiply to c and add to b.
- Trinomial (a≠1): use AC method or trial and error.
- Difference of squares: a² − b² = (a+b)(a−b).
- Perfect square trinomial: a² ± 2ab + b² = (a ± b)².
- Factor completely — keep factoring until no further factoring is possible.
6x² − 54 = 6(x²−9) = 6(x+3)(x−3) — factor GCF first, then difference of squares.
Practice — Lessons 5–8
Q5 · Multiple Choice
Factor completely: 4x² − 16.
Q6 · Short Answer
Factor x² − 5x + 6. Give the factored form as (x − ?)(x − ?).