Algebraic Expressions and Factoring

Front

What is an algebraic expression?

Back

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols (like +, -, *, /). For example, 3x + 5 is an algebraic expression.

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What does it mean to factor an expression?

Back

Factoring an expression means to break it down into simpler components (factors) that, when multiplied together, give the original expression. For example, factoring x^2 - 9 gives (x - 3)(x + 3).

Front

What is the difference between an equation and an expression?

Back

An equation states that two expressions are equal, using an equal sign (=). An expression does not have an equal sign and represents a value.

Front

What is the x-intercept of a graph?

Back

The x-intercept is the point where the graph crosses the x-axis, meaning the y-value is zero at that point.

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How do you find the domain of a function?

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The domain of a function is the set of all possible x-values that can be input into the function without causing any mathematical errors (like division by zero).

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What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables raised to whole number powers and coefficients. For example, 2x^3 - 4x + 7 is a polynomial.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^5 + 3x^2 - 2, the degree is 5.

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What is a coefficient in an algebraic expression?

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A coefficient is a numerical factor that multiplies a variable in an algebraic expression. For example, in 5x, 5 is the coefficient.

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What does it mean to simplify an expression?

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Simplifying an expression means to reduce it to its simplest form by combining like terms and eliminating unnecessary parentheses.

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What are like terms?

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