Unit 3 • Lessons 1–3 — Polynomial Operations (Quiz 1)
Review & Preview • Monomial × Polynomial • Two Binomials
Distributive Property
Combine Like Terms
Monomial × Polynomial
Binomial × Binomial (FOIL)
Special Products
Practice Set
Each question allows 2 attempts. Use the built-in whiteboard to show your work, then click Reveal Solution if needed.
1) Distributive Property
Simplify \(3(x+4)\).
Distribute 3 to both terms: \(3x+12\).
2) Monomial × Polynomial
Simplify \(2x(3x^2-5x+4)\).
Multiply each term by \(2x\): \(6x^3-10x^2+8x\).
3) Two Binomials (FOIL)
Simplify \((x+3)(x+2)\).
FOIL → \(x^2+2x+3x+6=x^2+5x+6\).
4) Binomials with Negatives
Simplify \((2x-3)(x-4)\).
\(2x^2-8x-3x+12=2x^2-11x+12\).
5) Monomial × Trinomial (Order in Standard Form)
Simplify \(-3x^2(4x-5+2x^3)\).
Multiply term-by-term: \(-12x^3+15x^2-6x^5\Rightarrow\) standard form \( -6x^5-12x^3+15x^2\).
6) Expand & Combine
Simplify \((x+2)(x-5) + (2x-1)(x+3)\).
\((x^2-3x-10)+(2x^2+5x-3)=3x^2+2x-13.\)
7) Special Product: Perfect Square
Simplify \((x+7)^2\).
Use \((a+b)^2=a^2+2ab+b^2\): \(x^2+14x+49\).
8) Special Product: Difference of Squares
Simplify \((3x+4)(3x-4)\).
\((a+b)(a-b)=a^2-b^2\Rightarrow (3x)^2-4^2=9x^2-16\).
Progress
Score: 0/8