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Rewrite a polynomial

EXAMPLE 1. Rewrite a polynomial. Write 15 x – x 3 + 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. 15 x – x 3 + 3.

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Rewrite a polynomial

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  1. EXAMPLE 1 Rewrite a polynomial 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. 15x – x3 + 3 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.

  2. Expression Is it a polynomial? Classify by degree and number of terms a. 9 Yes 0 degree monomial b. 2x2 + x – 5 Yes 2nd degree trinomial c. 6n4 – 8n No; variable exponent d. n– 2 – 3 No; variable exponent e. 7bc3 + 4b4c Yes 5th degree binomial EXAMPLE 2 Identify and classify polynomials Tell whetheris 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.

  3. EXAMPLE 3 Add polynomials Find the sum. a. (2x3 – 5x2 + x) + (2x2 + x3 – 1) b. (3x2 + x – 6) + (x2 + 4x + 10)

  4. + x3 + 2x2 – 1 EXAMPLE 3 Add polynomials SOLUTION a. Vertical format: Align like terms in vertical columns. (2x3 – 5x2 + x) 3x3 – 3x2 + x – 1 b. Horizontal format: Group like terms and simplify. (3x2 + x – 6) + (x2 + 4x + 10) = (3x2+ x2) + (x+ 4x) + (– 6+ 10) = 4x2 + 5x + 4

  5. 1. Write 5y – 2y2 + 9 so that the exponents decrease from left to right. Identify the degree and leading coefficient of the polynomial. 2. Tell whether y3 – 4y + 3 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. ANSWER – 2y2 +5y + 9 Degree: 2, Leading Coefficient: –2 ANSWER polynomial Degree: 3, trinomial EXAMPLE 1 for Examples 1,2, and 3 Rewrite a polynomial GUIDED PRACTICE

  6. 3. Find the sum. ANSWER = 8x3 + 4x2+ 2x – 6 EXAMPLE 3 for Example for Examples 1,2, and 3 Add polynomials GUIDED PRACTICE (5x3 + 4x – 2x) + (4x2 +3x3 – 6)

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