Integrated Math 2 / Unit 2: Polynomials and Factoring
2.2 Multiplying Polynomials
Notes
Multiply by distributing every term of one polynomial to every term of the other.
- Binomials (FOIL): $(x + 3)(x - 5) = x^2 - 5x + 3x - 15 = x^2 - 2x - 15$.
- Larger polynomials: $(2x - 1)(x^2 + 3x - 4) = 2x^3 + 6x^2 - 8x - x^2 - 3x + 4 = 2x^3 + 5x^2 - 11x + 4$.
- Squaring a binomial needs the middle term: $(x + 4)^2 = x^2 + 8x + 16$, not $x^2 + 16$.
- The product of a degree $m$ and a degree $n$ polynomial has degree $m + n$.
Practice
Multiply: $(x + 3)(x - 5)$.
FOIL gives $x^2 - 5x + 3x - 15$, and $-5x + 3x = -2x$.
Expand $(x + 4)^2$.
$(x + 4)(x + 4) = x^2 + 4x + 4x + 16$.
What is the degree of the product $(2x^3 + 1)(x^2 - 5x)$?
The leading terms multiply to $2x^5$, so the degree is $3 + 2 = 5$.
Ready for more? Take the Unit 2 test.