1 / 9

Sect. 5.3 Common Factors & Factoring by Grouping

Sect. 5.3 Common Factors & Factoring by Grouping. Definitions Factor Common Factor of 2 or more terms Factoring a Monomial into two factors Identifying Common Monomial Factors Factoring Out Common Factors Arranging 4 Term Polynomials into 2 Groups Factoring Out Common Binomials.

toviel
Télécharger la présentation

Sect. 5.3 Common Factors & Factoring by Grouping

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sect. 5.3 Common Factors & Factoring by Grouping • Definitions • Factor • Common Factor of 2 or more terms • Factoring a Monomial into two factors • Identifying Common Monomial Factors • Factoring Out Common Factors • Arranging 4 Term Polynomials into 2 Groups • Factoring Out Common Binomials 5.3

  2. What’s a Factor? product = (factor)(factor)(factor) … (factor) 84 is a product that can be expressed by many different factorizations: 84 = 2(42) or 84 = 7(12) or 84 = 4(7)(3) or 84 = 2(2)(3)(7) Only one example, 84 = 2(2)(3)(7), shows 84 as the product of prime integers. Factoringis the reverse of multiplication. 5.3

  3. Factoring Monomials • 12x3 also can be expressed in many ways:12x3 = 12(x3) 12x3 = 4x2(3x) 12x3 = 2x(6x2) • Usually, we only look for two factors • Your turn – factor these monomials into two factors: • 4a = • 2(2a)or4(a) • x3 = • x(x2) orx2(x) • 14y2 = • 14(y2) or14y(y)or7(2y2)or7y(2y)ory(14y)or … • 43x5 = • 43(x5)or43x(x4)orx3(43x2) or43x2(x3) or … 5.3

  4. Common Factors • Sometimes multi-termed polynomials can be factored • Looking for common factors in 2 or more terms … is the first step in factoring polynomials • Remember a(b + c) = ab + ac (distributive law) • Consider that a is a common factor of ab + acso we can factor ab + ac into a(b + c) • For x2 + 3x the only common factor is x , so • x2 + 3x = x(? + ?) = x(x + 3) • Another example: 4y2 + 6y – 10 • The common factor is 2 • 4y2 + 6y – 10 = 2(? + ? – ?) = 2(2y2 + 3y – 5) • Check by multiplying: 2(2y2) + 2(3y) – 2(5) = 4y2 + 6y – 10 5.3

  5. Find the Greatest Common Factor • 7a – 21 = • 7(? – ?) = • 7(a – 3) • 19x3 + 3x = • x(? + ?) = • x(19x2 + 3) • 18y3 – 12y2 + 6y = • 6y(? – ? + ?) = • 6y(3y2 – 2y + 1) 5.3

  6. Introduction to Factoring by Grouping:Factoring Out Binomials • x2(x + 7) + 3(x + 7) = • (x + 7)(? + ?) = • (x + 7)(x2 + 3) • y3(a + b) – 2(a + b) = • (a + b)(? – ?) = • (a + b)(y3 – 2) • You try: 2x2(x – 1) + 6x(x – 1) + 17(x – 1) = • (x – 1)(? + ? – ?) • (x – 1)(2x2 + 6x + 17) 5.3

  7. Factoring by Grouping • For polynomials with 4 terms: • Arrange the terms in the polynomial into 2 groupssuch thateach group has a common monomial factor • Factor out the common monomials from each group(the binomial factors produced will be either identical or opposites) • Factor out the common binomial factor • Example: 2c – 2d + cd – d2 • 2(c – d) + d(c – d) • (c – d)(2 + d) 5.3

  8. Factor by Grouping • 8t3 + 2t2 – 12t – 3 • 2t2(4t + 1)– 3(4t + 1) • (4t + 1)(2t2 – 3) • 4x3 – 6x2 – 6x + 9 • 2x2(2x – 3) – 3(2x – 3) • (2x – 3)(2x2 – 3) • y4 – 2y3 – 12y – 3 • y3(y – 2) – 3(4y + 1) • Oops –not factorable via grouping 5.3

  9. What Next? • Next time: Section 5.4 –Factoring Trinomials 5.3

More Related