Methods Of Factoring Trinomials - Lone Star College System
Methods of Factoring Trinomials6 x2 19 x 151. Trial and Error Method:This is the usual first method taught in most textbooks.The factor pairs of the leading coefficient and the constant term are determined.Factors of 61,62,3Factors of 151,153,5Then the possible binomial products are intelligently constructed and multiplied out. x 1 6 x 15 x 15 6 x 1 6 x 2 91x 15 x 3 6 x 5 6 x 2 23x 15 x 5 6 x 3 2 x 1 3x 15 2 x 15 3x 1 6 x 2 47 x 15 2 x 3 3x 5 6 x 2 19 x 15 2 x 5 3x 3 So 6 x2 19 x 15 2 x 3 3x 5 .
2. Listing and Pairing Method:This is a streamlined version of Trial and Error that I came up with.The factor pairs of the leading coefficient and constant term are listed. Then they arepaired up, multiplied, and added to produce the middle coefficient.Factors of 6Factors of 15101, 61 , 152, 33 , 59 19 So 6 x2 19 x 15 2 x 3 3x 5 .
3. Grouping Method:This method uses Factoring by Grouping which is usually taught as a method forfactoring 4-term polynomials. The trinomial is converted into an equivalent 4-termpolynomial, and then Factoring by Grouping is used.6 x2 19 x 15909, 106 x 2 9 x 10 x 15 6x2 9 x 10 x 15 3 x 2 x 3 5 2 x 3 2 x 3 3x 5 So 6 x2 19 x 15 2 x 3 3x 5 .
4. First Magic Method:This method begins like the Grouping Method, but it’s somewhat more efficient.6 x2 19 x 15909, 10 6 x 9 6 x 10 6All common factors are removed from each binomial.2 3 2 x 3 3x 5 6The fraction is reduced. 2 x 3 3x 5 So 6 x2 19 x 15 2 x 3 3x 5 .
5. Second Magic Method:This method begins like the Grouping Method, but it’s somewhat more efficient.6 x2 19 x 15909, 10 9 x 15 10 x 15 15All common factors are removed from each binomial.5 3 3x 5 2 x 3 15The fraction is reduced. 3x 5 2 x 3 So 6 x2 19 x 15 2 x 3 3x 5 .
6. First Black Magic Method:(Caution: You must remove all common factors first!)This method is a more efficient form of the Magic Method.6 x2 19 x 15909, 10 6 x 9 6 x 10 All common factors are removed from each binomial, and then discarded.2 3 2 x 3 3x 5 discardThis leads to 2 x 3 3x 5 So 6 x2 19 x 15 2 x 3 3x 5 .
7. Second Black Magic Method:(Caution: You must remove all common factors first!)This method is a more efficient form of the Magic Method.6 x2 19 x 15909, 10 9 x 15 10 x 15 All common factors are removed from each binomial, and then discarded.5 3 3x 5 2 x 3 discardThis leads to 3x 5 2 x 3 So 6 x2 19 x 15 2 x 3 3x 5 .
8. Bottoms-up Method: (Caution: You must remove all common factors first!)This method reduces the factoring of a general trinomial into the factoring of a trinomialwith a leading coefficient of 1.6 x2 19 x 1590Rewrite asAnd now factorx2 19 x 90 x 9 x 10 Now divide the two constant terms by the original leading coefficient.9 10 x x 6 6 Reduce the two constant terms. x 3 5 x 2 3 Now bring the denominators of the constant terms up as the leading coefficients of eachbinomial factor.3 5 x x 2 3 2 x 3 3x 5 So 6 x2 19 x 15 2 x 3 3x 5 .
9. The Box Method: (Caution: You must remove all common factors first!)This method is like the Grouping Method, but without actually grouping.6 x2 19 x 15909, 106x 210x9x15Now find all common factors for each row and each column.So 6 x2 19 x 15 2 x 3 3x 5 .3x52x6x 210x39x15
8. Bottoms-up Method: (Caution: You must remove all common factors first!) This method reduces the factoring of a general trinomial into the factoring of a trinomial with a leading coefficient of 1
Factoring Polynomials Martin-Gay, Developmental Mathematics 2 13.1 – The Greatest Common Factor 13.2 – Factoring Trinomials of the Form x2 bx c 13.3 – Factoring Trinomials of the Form ax 2 bx c 13.4 – Factoring Trinomials of the Form x2 bx c by Grouping 13.5 – Factoring Perfect Square Trinomials and Difference of Two Squares
Factoring Trinomials Guided Notes . 2 Algebra 1 – Notes Packet Name: Pd: Factoring Trinomials Clear Targets: I can factor trinomials with and without a leading coefficient. Concept: When factoring polynomials, we are doing reverse multiplication or “un-distributing.” Remember: Factoring is the process of finding the factors that would .
Move to the next page to learn more about factoring and how it relates to polynomials. [page 2] Factoring Trinomials by Grouping There is a systematic approach to factoring trinomials with a leading coefficient greater than 1 called . If you need a refresher on factoring by grouping
241 Algebraic equations can be used to solve a large variety of problems involving geometric relationships. 5.1 Factoring by Using the Distributive Property 5.2 Factoring the Difference of Two Squares 5.3 Factoring Trinomials of the Form x2 bx c 5.4 Factoring Trinomials of the Form ax2 bx c 5.5 Factoring, Solving Equations, and Problem Solving
Factoring Trinomials Factoring trinomials, expressions of the form !"# %" &, is an important skill. Trinomials can be factored if they are the product of two binomials. The two main keys to factoring trinomials are: (1) the ability to quickly and accurately multiply binomials (FOIL) and (2) the ability to work with signed numbers.
Factoring Trinomials This objective covers the factoring of trinomials, by arranging terms in descending degree and inspection of signs to locate signs in the factors. Factoring Trinomials by Grouping This objective covers polynomials with four or more terms, the method of factoring
Factoring Trinomials in One Step THE INTRODUCTION To this point you have been factoring trinomials using the product and sum numbers with factor by grouping. That process works great but requires a number of written steps that sometimes makes it slow and space consuming. Consider the steps involved when factoring 8x2 10x – 3:
Factoring . Factoring. Factoring is the reverse process of multiplication. Factoring polynomials in algebra has similar role as factoring numbers in arithmetic. Any number can be expressed as a product of prime numbers. For example, 2 3. 6 Similarly, any
