Category 1 - Flashcard 19

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you expand the expression (x + 2)(x^2 - 3x + 7)?

Back

To expand, apply the distributive property: x(x^2 - 3x + 7) + 2(x^2 - 3x + 7) = x^3 - 3x^2 + 7x + 2x^2 - 6x + 14 = x^3 - x^2 + x + 14.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. Example: 3x^2 + 2x + 1.

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 4x^3 + 2x^2 + 5, the degree is 3.

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they have the same value for all values of the variable(s) involved.

Front

How do you factor the expression 72x^2 - 9x?

Back

To factor, first find the greatest common factor (GCF), which is 9x. Then, factor it out: 72x^2 - 9x = 9x(8x - 1).

Front

What is the process of simplifying an expression?

Back

Simplifying an expression involves combining like terms and reducing fractions to their simplest form.

Front

What are like terms in algebra?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms.

Front

What is the difference between a monomial, binomial, and polynomial?

Back

A monomial has one term (e.g., 3x), a binomial has two terms (e.g., 3x + 2), and a polynomial has multiple terms (e.g., 3x^2 + 2x + 1).

Front

What is the zero product property?

Back

The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero. For example, if ab = 0, then a = 0 or b = 0.