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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. R - Algebra ReviewProblema R.3.1
Capitolo 1, Problema R.3.1

CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The polynomial 2x⁵ - x + 4 is a trinomial of degree _________.

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Identify the degree of the polynomial by looking at the term with the highest exponent. The degree of a polynomial is the highest power of the variable in the expression.
In the polynomial \(2x^{5} - x + 4\), observe the exponents of each term: \(5\) in \$2x^{5}$, \(1\) in $-x$, and \(0\) in the constant term \(4\).
Since the highest exponent is \(5\), the degree of the polynomial is \(5\).
Note that the polynomial has three terms: \$2x^{5}\(, \)-x$, and \(4\), which makes it a trinomial (a polynomial with exactly three terms).
Therefore, the polynomial \(2x^{5} - x + 4\) is a trinomial of degree \(5\).

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Polynomial Degree

The degree of a polynomial is the highest power of the variable in the expression. It indicates the polynomial's order and helps determine its behavior and graph shape. For example, in 2x⁵ - x + 4, the highest exponent is 5, so the degree is 5.
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Polynomial Terms

A polynomial consists of terms separated by plus or minus signs. Each term includes a coefficient and a variable raised to a non-negative integer exponent. The number of terms defines if it is a monomial, binomial, trinomial, etc. Here, 2x⁵ - x + 4 has three terms, making it a trinomial.
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Trinomial Definition

A trinomial is a polynomial with exactly three terms. These terms can have different degrees and coefficients. Recognizing the number of terms helps classify polynomials and understand their structure, which is essential for operations like factoring or graphing.
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CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. x² + 10xy + 25y² A. (x + 5y) (x - 5y) b. x² - 10xy + 25y² B. (x + 5y)² c. x² - 25y² C. (x - 5y)² d. 25y² - x² D. (5y + x) (5y - x)

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