Rewrite 4-5x-x2+6x3 in descending powers of x.

Ch. 3 - Polynomial and Rational Functions

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Blitzer 8th Edition

Ch. 3 - Polynomial and Rational Functions

문제 114

4장, 문제 114

Rewrite 4-5x-x²+6x³ in descending powers of x.

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Identify the powers of x in each term of the polynomial: 4 (which is x^0), -5x (which is x^1), -x^2, and 6x^3.

Recall that descending powers of x means arranging the terms starting from the highest power of x to the lowest power.

Determine the order of powers from highest to lowest: x^3, x^2, x^1, and x^0.

Rewrite the polynomial by placing the terms in order of descending powers: start with the term containing x^3, then x^2, then x^1, and finally the constant term.

Express the polynomial as

6x x^{3} - x^{2} - 5x + 4

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Polynomial Terms and Powers

A polynomial is an expression consisting of variables raised to non-negative integer powers, combined using addition or subtraction. Each term includes a coefficient and a power of the variable, such as x^3 or x^2. Understanding the structure of polynomial terms is essential for rearranging them.

Descending Order of Powers

Writing a polynomial in descending order means arranging its terms from the highest power of the variable to the lowest. This standard form helps in comparing, adding, or subtracting polynomials and is crucial for clarity and further operations.

Combining Like Terms

Like terms have the same variable raised to the same power and can be combined by adding or subtracting their coefficients. Recognizing and combining like terms simplifies the polynomial before ordering it, ensuring the expression is in its simplest form.