Flashcard 4.2 (Polynomial Operations 1)

Front

What is the result of (3 - 2x + 2x²) - (4x - 5 + 3x²)?

Back

-x² - 6x + 8

Front

Calculate the product of (3r - 4)(7r - 5).

Back

21r² - 43r + 20

Front

What is the sum of (3y² + y³ - 5) + (4y² - 4y + 2y³ + 8)?

Back

3y³ + 7y² - 4y + 3

Front

Find the difference: (7k + 2k³ - 8k⁴) - (4k³ - 5k + 4k² - 7k⁴).

Back

-k⁴ - 2k³ - 4k² + 12k

Front

Multiply: (b + 3)(b² + 2b + 1).

Back

b³ + 5b² + 7b + 3

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

Define the degree of a polynomial.

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

Explain the process of polynomial addition.

Back

To add polynomials, combine like terms by adding their coefficients.

Front

Explain the process of polynomial subtraction.

Back

To subtract polynomials, change the signs of the terms in the polynomial being subtracted and then combine like terms.