Higher Degree Polynomials Study Guide

What is a Polynomial?

A polynomial is an algebraic expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Degree of a Polynomial

The degree of a polynomial is the highest power of the variable in the polynomial.

Higher Degree Polynomials

Higher degree polynomials are polynomials with a degree greater than two. They can be of the form:

Quadratic (degree 2): \[ax^2 + bx + c\]
Cubic (degree 3): \[ax^3 + bx^2 + cx + d\]
Quartic (degree 4): \[ax^4 + bx^3 + cx^2 + dx + e\]
Quintic (degree 5): \[ax^5 + bx^4 + cx^3 + dx^2 + ex + f\]
And so on...

Operations with Higher Degree Polynomials

Operations on higher degree polynomials involve addition, subtraction, multiplication, and division. It's important to understand how to combine like terms, factor, and use long division to simplify and solve problems involving higher degree polynomials.

Graphing Higher Degree Polynomials

When graphing higher degree polynomials, it's important to identify the behavior of the polynomial for large positive and negative values of x, find the x-intercepts (real roots), and determine the end behavior of the graph.

Study Tips

Understand the concept of degree and leading coefficient of a polynomial.
Practice combining like terms and simplifying expressions involving higher degree polynomials.
Learn the techniques for factoring and solving equations with higher degree polynomials.
Practice graphing higher degree polynomials to understand their behavior.

Remember to always check your understanding by solving practice problems and seeking help from your teacher or tutor when needed.

◂Math Worksheets and Study Guides Seventh Grade. Measurement, Perimeter, and Circumference

Study Guide

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

The resources above cover the following skills:

Geometry (NCTM)

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.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.