2.1-2.4 Polynomial Operations -Dabbous

Front

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

Back

3y³ + 7y² - 4y + 3

Front

How do you multiply the polynomials (2x + 3) and (x² + 4x + 1)?

Back

2x³ + 11x² + 14x + 3

Front

What is the result of squaring the binomial (2x + 3)?

Back

4x² + 12x + 9

Front

What is the product of the polynomials (4x + 1) and (5x - 2)?

Back

20x² - 3x - 2

Front

How do you subtract the polynomial (x⁴ + 5x³ + 8x² + x + 5) from (5x⁴ - 4x³ - 2x² + x - 19)?

Back

4x⁴ - 9x³ - 10x² - 24

Front

What is the degree of the polynomial 3y³ + 7y² - 4y + 3?

Back

The degree is 3, which is the highest exponent of the variable y.

Front

Define polynomial addition.

Back

Polynomial addition involves combining like terms from two or more polynomials to form a new polynomial.

Front

What is the distributive property in the context of polynomial multiplication?

Back

The distributive property states that a(b + c) = ab + ac, which is used to multiply a polynomial by a binomial.

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as (2x + 3).

Front

Explain how to combine like terms in a polynomial.

Back

To combine like terms, add or subtract the coefficients of terms that have the same variable raised to the same power.