9.1 Adding and Subtracting Polynomials. The terms of a polynomial may appear in any order. However, in standard form, the terms of a polynomial are.

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Presentation transcript:

9.1 Adding and Subtracting Polynomials

The terms of a polynomial may appear in any order. However, in standard form, the terms of a polynomial are ordered from left to right in descending order, which means from the greatest exponent to the least.

Some polynomial expressions have special names that are determined either by their degree or by the number of terms, as illustrated in the table.

Ex 1. Classify each polynomial by degree and by number of terms. First, combine Like terms with the same letter and exponent power. Second, what is the highest exponent and name it by the degree. Third, count how many terms there are and name it. a.2x 3 - 3x + 4x 3 b. –2x 3 + 3x 4 + 2x c. x x - 2x 3 d. 3x – x 3 – 6x 5 e. 5x + 2x 3 + 4x 2 f. x 5 – 4x 3 - x 5 + 3x 2 + 4x 3 6x 3 – 3xCubic Binomial3x 4 + 5Quartic Binomial Cubic Polynomial 2x 3 – 6x 5 + 2Quintic Trinomial Cubic Trinomial3x 2 Quadratic Monomial

Adding Polynomials Polynomials can be added in vertical and horizontal form. In vertical form, align the like terms and add. In horizontal form, regroup like terms and add.

Ex. 4a. (-2x 2 – 3x 3 + 5x + 4) + (-2x 3 + 7x – 6)

Ex. 5

Subtracting Polynomials Recall that subtraction can be modeled by adding the opposite.

Ex 3. Find the difference and write it from highest to lowest power.