Required Resources
Read/review the following resources for this activity:
- OpenStax Textbook Readings
- Lesson in Canvas
- Assignments in Knewton
- Factoring Trinomials with a Leading Coefficient of 1
- Factoring Trinomials with a Leading Coefficient Other than 1
- Factoring Special Products
- Choosing a Factoring Strategy
- Solving Quadratic Equations by Factoring
- Solving Polynomial Equations by Factoring
Initial Post Instructions
This week we continue our study of factoring. As you become more familiar with factoring, you will notice there are some special factoring problems that follow specific patterns. These patterns are known as:
- a difference of squares;
- a perfect square trinomial;
- a difference of cubes; and
- a sum of cubes.
Choose two of the forms above and explain the pattern that allows you to recognize the binomial or trinomial as having special factors. Illustrate with examples of a binomial or trinomial expression that may be factored using the special techniques you are explaining. Make sure that you do not use the same example a classmate has already used!
ANSWER:
I have chosen to talk about; a perfect square trinomial and a sum of cubes. Before I talk about the various patterns of recognizing trinomial expressions using special techniques, let’s first understand the definition of a perfect square trinomial and a sum of cubes.
A trinomial is an addition of 3 monomial expressions. A perfect square trinomial in basic terms is a unique group of polynomials that can be factored or distributed. On the other hand, a sum of cubes is a two-term format in which both expressions have the same symbol.
To recognize a trinomial, we want to first ask if we are able to combine the like terms together, count the number of terms in the expression. Using special formulas for a perfect square trinomial such as:
ax2 + bx + c is a perfect trinomial if it satisfies the condition b2 = 4ac
ax2+2abx +b2 = (ax + b)2,
ax2 -2abx +b2 = (ax – b)2
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