Operations with Polynomials

1. x^2 + x - 6 + x^2 + 4x + 10

Annotations:

• x^2 + x^2 + x + 4x - 6 + 10=

1. x^2 + x^2 + x + 4x - 6 + 10 = 2x^2 + 5x + 4

1. 4x(x - 2) = 4x^2 - 8x

1. (x + 2)(x + 5) = x^2 + 5x + 2x + 10
   1. Combine like terms: x^2 + 7x + 10

1. Step 1: Distribute the first term of the binomial to each term in the trinomial.
   1. x(x^2 - 4x + 1) = x^3 -4x^2 + 1x
2. Step 2: Distribute the second term of the binomial to each term in the trinomial.
   1. 3(x^2 - 4x + 1) = 3x^2 -12x + 3
   2. Step 3: Combine like terms: x^3 - 4x^2 + 3x^2 + 1x - 12x + 3= x^3 - x^2 - 11x + 3

1. If it has two terms, are they both perfect squares?
   1. Yes: (a^2-b^2) Example: x^2 - 81 = (x + 9)(x - 9)
   2. No: Example: 8x - 10 = 2(4x - 5)
2. If it has three terms, use "reverse foil"
   1. (x + p)(x + q) Example: x^2 + 10x + 16 = (x + 8)(x + 2)
   2. (x - p)(x - q) Example: x^2 - 8x + 15 = (x - 3)(x - 5)
   3. (x + p)(x - q) Example: x^2 + 5x - 14 = (x + 7)(x - 2)

1. (4x^2 -3x + 5) - (-3x^2 - x - 8) = 4x^2 - 3x + 5 - 3x^2 + x + 8

1. 4x^2 - 3x^2 - 3x + x + 5 - 8 = x^2 - 2x + 13