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. For example, 2x + 3 is an algebraic expression.

Front

What does the term 'x-intercept' mean?

Back

The x-intercept is the point where a graph crosses the x-axis. It occurs when the value of y is zero.

Front

What is the solution of a system of linear equations?

Back

The solution of a system of linear equations is the point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

What does it mean if a system of equations has 'infinitely many solutions'?

Back

It means that the equations represent the same line, and there are countless points (x, y) that satisfy both equations.

Front

How do you factor the expression x² + 7x + 12?

Back

To factor x² + 7x + 12, find two numbers that multiply to 12 and add to 7. The factors are (x + 3)(x + 4).

Front

What is the purpose of graphing an expression?

Back

Graphing an expression helps visualize its behavior, identify intercepts, and find solutions to equations.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.

Front

What does it mean for two equations to be 'consistent'?

Back

Two equations are consistent if they have at least one solution, meaning their graphs intersect at one or more points.

Front

What is a quadratic expression?

Back

A quadratic expression is a polynomial of degree 2, typically in the form ax² + bx + c, where a, b, and c are constants.