Algebra 1 9.1

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Simplify the expression. 1. 5x + 4(2x + 7) 2. 9x – 6(x + 2) + 3 Bell Ringer WarmUps

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Rewrite a polynomial EXAMPLE 1 Write 15x – x3 + 3 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial. SOLUTION Consider the degree of each of the polynomial’s terms. The polynomial can be written as – x3 +15 + 3. The greatest degree is 3, so the degree of the polynomial is 3, and the leading coefficient is –1. 15x – x3 + 3

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Tell whether is a polynomial. If it is a polynomial, find its degree and classify it by the number of its terms. Otherwise, tell why it is not a polynomial. EXAMPLE 2 Identify and classify polynomials

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EXAMPLE 3 Add polynomials a. (2x3 – 5x2 + x) + (2x2 + x3 – 1) a. Vertical format: Align like terms in vertical columns. (2x3 – 5x2 + x) 3x3 – 3x2 + x – 1

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EXAMPLE 3 Add polynomials b. Horizontal format: Group like terms and simplify. (3x2 + x – 6) + (x2 + 4x + 10) = = 4x2 + 5x + 4 (3x2 + x2) + (x + 4x) + (– 6 + 10) b. (3x2 + x – 6) + (x2 + 4x + 10)

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Rewrite a polynomial EXAMPLE 1 GUIDED PRACTICE for Examples 1,2, and 3

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EXAMPLE 3 Add polynomials (5x3 + 4x – 2x) + (4x2 +3x3 – 6) GUIDED PRACTICE for Example for Examples 1,2, and 3

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EXAMPLE 4 Subtract polynomials Find the difference. a. (4n2 + 5) – (–2n2 + 2n – 4) a. (4n2 + 5) 4n2 + 5 6n2 – 2n + 9 Vertical Format

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EXAMPLE 4 Subtract polynomials b. (4x2 – 3x + 5) – (3x2 – x – 8) = = (4x2 – 3x2) + (–3x + x) + (5 + 8) = x2 – 2x + 13 4x2 – 3x + 5 – 3x2 + x + 8 b. (4x2 – 3x + 5) – (3x2 – x – 8) Horizontal Format Distribute the negative Combine like terms

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EXAMPLE 4 Subtract polynomials a. (4x2 – 7x) – (5x2 + 4x – 9) GUIDED PRACTICE for Examples 4 and 5 4x2 – 7x – 5x2 – 4x + 9

Homework 9.1 : 

Homework 9.1 Pages: 557 – 559 Exs. 4 – 34 even, 38, 43