Breaking 'Em Up (1 of 2)
- Author:
- Jaime Dianzon
- Topic:
- Algebra
How do you break 'em up?
OBJECTIVE: To learn how to factor a Type I General Quadratic Trinomial (a = 1)
In a previous lesson, you learned how to factor a special trinomial—the Perfect Square Trinomial.
Identifying Twins: https://www.geogebra.org/m/h44emf4r
In this lesson, you'll learn how to factor the first of two types of General Quadratic Trinomials (Type I), one in which a = 1 in the quadratic expression, ax2 + bx + c. The other type (Type II), as you may have guessed, is one in which a ≠ 1. If a quadratic trinomial has no indicated coefficient in the x2 term, it belongs to the first type, which is the topic of today's lesson.
The first step in any factoring problem, as has been mentioned countless times before, is to factor out any Greatest Common Factor (GCF) or Common Monomial Factor (CMF) from the terms of the polynomial. Failure to do so accounts for most errors in factoring—incomplete factorization or even incorrect factorization.
After the GCF/CMF has been factored out, the remaining polynomial may be factored as a special binomial or trinomial, or as a Type I or Type II general quadratic trinomial, if there are only two or three terms left. More advanced techniques will be used for polynomials with more than three terms.
HOW TO FACTOR TYPE I GENERAL QUADRATIC TRINOMIALS (a = 1):
1. Make sure to arrange the trinomial in general form: ax2 + bx + c.
2a. If the third term is positive, look for factors of c whose sum is b. Both factors will take the sign of the middle term (same signs).
2b. If the third term is negative, look for factors of c whose difference is b. The bigger factor will take the sign of the middle term, while the smaller factor takes the opposite sign (different signs).
3. Generate the factors systematically to avoid any possible omissions. Watch the video below for examples.
The applet below can be used to practice factoring Type I General Quadratic Trinomials (a = 1).
Solve the problems mentally or on a separate sheet, and then verify your answer by clicking "Check Factors."
Note: A few problems are Perfect Square Trinomials.
Applet by Steve Phelps
Below is a set of problems that require you to factor Type I General Quadratic Trinomials (a = 1).
Check the Answer Box below for the correct answers.
Factoring Type I General Quadratic Trinomials (a = 1)
ANSWER BOX:
Check out the answers to the above problems here.
TODAY you learned how to factor Type I General Quadratic Trinomials (a = 1).
In future lessons, you'll learn how to factor Type II General Quadratic Trinomials (a ≠ 1) and other polynomials. Did you have FUN today?