Flashcard 4 - Operations on polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 2x^2 + 3x + 5 is a polynomial.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees. For example, factoring 2x^2 + 5x + 3 gives (2x + 3)(x + 1).

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms. For example, 4x^3 + 2x^2 - x + 7 is in standard form.

Front

How do you factor the polynomial 2x^2 + 17x + 21?

Back

To factor 2x^2 + 17x + 21, look for two numbers that multiply to (2*21) = 42 and add to 17. The factors are 14 and 3, so it can be factored as (2x + 3)(x + 7).

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern that states a^2 - b^2 = (a + b)(a - b). For example, x^2 - 9 = (x + 3)(x - 3).

Front

What is the result of simplifying (5n - 8)(5n + 8)?

Back

The result of simplifying (5n - 8)(5n + 8) is 5n^2 - 64, using the difference of squares formula.

Front

How do you simplify -3x^2(7x^2 - x + 4)?

Back

Distribute -3x^2 to each term: -3x^2 * 7x^2 = -21x^4, -3x^2 * (-x) = 3x^3, -3x^2 * 4 = -12x^2. So, the result is -21x^4 + 3x^3 - 12x^2.

Front

What is the FOIL method in multiplying binomials?

Back

The FOIL method stands for First, Outside, Inside, Last. It is used to multiply two binomials. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is the result of simplifying (3x - 1)(x + 5)?

Back

The result of simplifying (3x - 1)(x + 5) is 3x^2 + 14x - 5, using the distributive property.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^2, 4 is the coefficient.