Factoring

What is Factoring?

Factoring is the process of finding the factors of a given algebraic expression. Factors are the numbers or algebraic expressions that can be multiplied together to get the original expression. Factoring is an important skill in algebra and is used in various mathematical operations, such as simplifying expressions, solving equations, and graphing functions.

Types of Factoring

There are different methods of factoring, including:

Common Factor Factoring: In this method, we look for the greatest common factor of all the terms in the expression and factor it out.
Factoring by Grouping: When a polynomial has four terms, we can group pairs of terms together and factor out a common factor from each pair.
Factoring Trinomials: This involves factoring quadratic trinomials of the form ax^2 + bx + c, where a, b, and c are constants.
Difference of Squares: This method involves factoring expressions of the form a^2 - b^2.
Factoring Perfect Square Trinomials: These are trinomials that can be factored into the square of a binomial.

Why is Factoring Important?

Factoring is important because it helps us simplify complex expressions, solve equations, and understand the behavior of functions. It is a fundamental skill in algebra and is widely used in various areas of mathematics and science.

Study Guide for Factoring

Here are some steps to follow when factoring algebraic expressions:

Identify the type of factoring method needed based on the form of the expression.
Look for common factors and factor them out if possible.
Use the appropriate method to factor the expression completely.
Check your factored expression by multiplying the factors to ensure they produce the original expression.

Practice factoring various types of expressions, including polynomials, trinomials, and special cases such as perfect square trinomials and the difference of squares. This will help you develop a strong understanding of factoring techniques.

Remember to also review the properties of numbers and algebraic expressions, as they are essential for factoring effectively.

By mastering the skill of factoring, you will be better equipped to solve equations, simplify expressions, and analyze mathematical relationships.

Now that you have a comprehensive understanding of factoring, you can apply these techniques to solve various mathematical problems and explore more advanced topics in algebra and beyond.

◂Math Worksheets and Study Guides Seventh Grade. Exploring Area and Surface Area

Study Guide

Exploring Area and Surface Area

Worksheet/Answer key

Exploring Area and Surface Area

Worksheet/Answer key

Exploring Area and Surface Area

Worksheet/Answer key

Exploring Area and Surface Area

Worksheet/Answer key

Exploring Area and Surface Area

The resources above cover the following skills:

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.

Grade 7 Curriculum Focal Points (NCTM)

Measurement and Geometry and Algebra: Developing an understanding of and using formulas to determine surface areas and volumes of three-dimensional shapes

By decomposing two- and three-dimensional shapes into smaller, component shapes, students find surface areas and develop and justify formulas for the surface areas and volumes of prisms and cylinders. As students decompose prisms and cylinders by slicing them, they develop and understand formulas for their volumes (Volume = Area of base x Height). They apply these formulas in problem solving to determine volumes of prisms and cylinders. Students see that the formula for the area of a circle is plausible by decomposing a circle into a number of wedges and rearranging them into a shape that approximates a parallelogram. They select appropriate two- and three-dimensional shapes to model real-world situations and solve a variety of problems (including multi-step problems) involving surface areas, areas and circumferences of circles, and volumes of prisms and cylinders.