# Operations with Polynomials

Mind Map by ldefeo2005, updated more than 1 year ago
 Created by ldefeo2005 about 4 years ago
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## Resource summary

Operations with Polynomials
1 Adding Polynomials (x^2 + x - 6) + (x^2 + 4x + 10)
1.1 Step 1: Rewrite polynomials without parenthesis
1.1.1 x^2 + x - 6 + x^2 + 4x + 10
1.2 Step 2: Combine like terms.

Annotations:

• x^2 + x^2 + x + 4x - 6 + 10=
1.2.1 x^2 + x^2 + x + 4x - 6 + 10 = 2x^2 + 5x + 4
2 Multiplying Polynomials
2.1 For a monomial times a binomial, use the distributive property
2.1.1 4x(x - 2) = 4x^2 - 8x
2.2 For a binomial times a binomial, use FOIL (x + 2)(x + 5)
2.2.1 (x + 2)(x + 5) = x^2 + 5x + 2x + 10
2.2.1.1 Combine like terms: x^2 + 7x + 10
2.3 For a binomial times a trinomial (x + 3)(x^2 - 4x + 1)
2.3.1 Step 1: Distribute the first term of the binomial to each term in the trinomial.
2.3.1.1 x(x^2 - 4x + 1) = x^3 -4x^2 + 1x
2.3.2 Step 2: Distribute the second term of the binomial to each term in the trinomial.
2.3.2.1 3(x^2 - 4x + 1) = 3x^2 -12x + 3
2.3.2.2 Step 3: Combine like terms: x^3 - 4x^2 + 3x^2 + 1x - 12x + 3= x^3 - x^2 - 11x + 3
3 Factoring Polynomials a=1
3.1 Step 1: If possible, factor out the greatest common factor. Example: 3x^2 + 6x - 18=3(x^2 + 5x - 6)
3.1.1 If it has two terms, are they both perfect squares?
3.1.1.1 Yes: (a^2-b^2) Example: x^2 - 81 = (x + 9)(x - 9)
3.1.1.2 No: Example: 8x - 10 = 2(4x - 5)
3.1.2 If it has three terms, use "reverse foil"
3.1.2.1 (x + p)(x + q) Example: x^2 + 10x + 16 = (x + 8)(x + 2)
3.1.2.2 (x - p)(x - q) Example: x^2 - 8x + 15 = (x - 3)(x - 5)
3.1.2.3 (x + p)(x - q) Example: x^2 + 5x - 14 = (x + 7)(x - 2)
4 Subtracting Polynomials (4x^2 -3x + 5) - (3x^2 - x - 8)
4.1.1 (4x^2 -3x + 5) - (-3x^2 - x - 8) = 4x^2 - 3x + 5 - 3x^2 + x + 8
4.2 Step 2: Combine like terms
4.2.1 4x^2 - 3x^2 - 3x + x + 5 - 8 = x^2 - 2x + 13

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