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.

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.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 3x^4 + 2x^2, the degree is 4.

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. For example, in 5x^3 + 2x^2, the leading coefficient is 5.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the distributive property (FOIL method): First, Outer, Inner, Last. For example, (x + 2)(x + 3) = x^2 + 5x + 6.

Front

What is the difference of squares?

Back

The difference of squares is a special factoring pattern: a^2 - b^2 = (a + b)(a - b). For example, x^2 - 49 = (x + 7)(x - 7).

Front

What is a quadratic polynomial?

Back

A quadratic polynomial is a polynomial of degree 2, typically in the form ax^2 + bx + c, where a, b, and c are constants.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation: x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a polynomial that can be expressed as the square of a binomial, such as (a + b)^2 = a^2 + 2ab + b^2.