Lesson 1: 4-1 Operations with Polynomials

1. Look at the exponent laws. Which ones are similar?
2. Redraw the Concept Summary as a spider chart or concept chart in any shape that makes sense to you. Write each exponent law and at least one example of each type.
3. Expand your concept summary by including an example of each exponent law using small real numbers for the base and exponent. How does using real numbers help you to make sense of the exponent laws?

Simplify
Degree of a Polynomial

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

SAT questions related to polynomial operations: 7-3-2, 6-4-1, 4-3-5, 3-4-6, 1-3-5, 4-4-2, 3-4-33, 8-3-5; dividing polynomials: 7-3-13, 2-3-15

When multiplying or dividing powers of variables, be sure that he base is the same. Add the exponents if multiplying powers of the same variable, and subtract them if dividing powers.

The light from the Sun takes approximately 8 minutes to reach Earth. So if you are outside right now, you are basking in sunlight that the Sun emitted approximately 8 minutes ago. Light travels very fast, at a speed of about 3x10^8 meters per second. How long would it take light to get here from the Andromeda galaxy, which is approximately 2.367x10^21 meters away?

Suggest that students return to the basic definitions for exponents rather than just memorizing rules. For example, they can derive the rule for multiplying quantities such as x^2 times x^3 by rewriting the problem as x times x times x times x times x.

Have students write their own summary of the properties of powers, such as "to multiply expressions with exponents, you add the exponents; to divide, you subtract the exponents."

McGraw Hill resources

McGraw Hill resources