Lesson 3: Common Factors and Factoring Trinomials: Summary

Math 10C Module 3 Lesson 3

Module 3: Polynomials

Lesson 3 Summary

In Lesson 3 you investigated the following questions:

How are polynomial-factoring strategies similar to strategies used to obtain the prime factorization of a whole number?
How can you tell if a polynomial is factored correctly?

In this lesson you learned how to find the common factors of a polynomial. Like the prime factorization that you learned in Module 2, you can also break monomials into their prime and variable factors. By doing so, you can apply the same techniques for generating the greatest common factor that you did with whole numbers. Alternatively, you could also list all of the factors of each term in a polynomial and select the greatest common factor from the lot.

In the previous lesson you verified your solutions by substituting a known numerical value to see if both sides of the expression would yield the same value. One of the key ideas in this lesson is that factoring is the reverse process of multiplying polynomials. Therefore, an alternate method for checking that the obtained factors are correct is to multiply the factors together. If the result is equal to the original polynomial, then the factors are correct.

In the next lesson you will build upon the factoring strategies you have learned so far. You will explore strategies that can help you to factor trinomials of the form ax2 + bx + c, where a ≠ 1.