24-25 Adv Alg2 5-1 FLASHCARD - Operations with Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

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

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial, then combine like terms.

Front

What is the result of (5x + 2)(x^2 - 3x + 6)?

Back

5x^3 - 13x^2 + 24x + 12.

Front

What does it mean to simplify an expression?

Back

To simplify an expression means to combine like terms and reduce it to its simplest form.

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign to each term of the polynomial being subtracted, then combine like terms.

Front

What is the result of (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1)?

Back

-8n^2 - 8n + 3.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used when dividing by a linear factor.

Front

What is long division in polynomials?

Back

Long division in polynomials is a method used to divide a polynomial by another polynomial, similar to long division with numbers.

Front

What is the result of (x^2 + 30x - 64) ÷ (x - 2)?

Back

x + 32.